https://ejpam.com/index.php/ejpam/issue/feedEuropean Journal of Pure and Applied Mathematics2019-05-19T08:51:13+00:00Editorial Office, EJPAMeditor@ejpam.comOpen Journal Systems<h3>Welcome</h3><p align="justify"><strong></strong></p><p align="justify"><em>European Journal of Pure and Applied Mathematics</em> is an international electronic journal which is devoted to original research in the field of pure and applied mathematics and their teaching and learning. The aim of the journal is to provide a medium by which a wide range of experience can be exchanged among researchers from diverse fields such as engineering, natural sciences or social sciences. This journal publishes high quality researches in the fields of contemporary pure and applied mathematics with a broad range of topics including algebra, topology, number theory, approximation theory, mathematical methods in operational research, theoretical statistics and econometrics, and theoretical computer science.</p><p align="justify">Another feature of the journal is to publish papers on mathematics education which contribute to the improvement of mathematics teaching and learning for students from upper secondary/high school level through to university first degree level. Although the journal focuses on the original research articles, it also welcomes reviews and short notes. All submitted papers are peer-reviewed.</p><p align="justify"><strong>Editorial Board</strong></p><p align="justify">The<strong> </strong>Editorial Board consists of prominent scientists as some are Nobel Laureates.</p><p align="justify">See<strong></strong> <a href="/index.php/ejpam/about/editorialTeam">editorial board</a> details.</p><p align="justify"><strong>Readership</strong></p><p>The journal is a rostrum for the audience of mathematicians, operational researchers, statisticians, econometricians, computer scientists, mathematics educators and all scientists using mathematics.</p><p><strong>Journal Impact </strong></p><p class="MsoNormal">Papers: 439, Citations: 2,132, <strong>Cites/paper (Impact Factor): 4.86</strong>. </p><p>The current EJPAM Journal impact is calculated using Harzing's Publish or Perish software that employs Google Scholar on 22.01.2018.</p><p><strong>Abstracted/Indexed in:</strong></p><p align="justify">Thomson Reuters (Clarivate Analytics) Emerging Sources Citation Index (ESCI), Web of Science, Mathematical Reviews, Zentralblatt MATH, EBSCO, Chambridge Scientific Abstracts, IndexCopernicus™, International Abstracts in Operations Research, Ulrich's Periodicals Directory, <a title="Arastirmax Bilimsel Yayın İndeksi" href="http://www.arastirmax.com/dergi/european-journal-pure-and-applied-mathematics" target="_blank" rel="noopener">Arastirmax</a>, CrossRef</p> <p align="justify">ISSN:1307-5543 <br />Inaugural publication: January 2008 <br />The journal is quarterly</p><p align="justify"><strong>Publisher</strong></p><p align="justify">European Journal of Pure and Applied Mathematics is published by<strong> New York Business Global</strong>, USA.</p>https://ejpam.com/index.php/ejpam/article/view/3415Correction to the Article: "An Introduction to the Theory of Hyperlattices"2019-04-29T17:35:36+00:00Niovi Kehayopulunkehayop@math.uoa.grThe definition of hyperlattices introduced in Mathematica Balkanica, 1977 by Mittas and Konstantinidou in their paper ``An introduction to the theory of hyperlattices" should be corrected. As a result, the definition of distributive and modular hyperlattices introduced by Konstantinidou and Serafimidis should be also corrected. In the present paper we give a corrected form of these definitions and some examples to show that these definitions work.2019-04-29T17:35:36+00:00Copyright (c) 2019 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3394Some Characterizations of β-paracompactness in Ideal Topological Space2019-04-29T17:35:36+00:00Esra Dalan Yıldırımesra.dalan@yasar.edu.trOya Bedre Özbakıroya.ozbakir@ege.edu.trAysegul Caksu Guleraysegul.caksu.guler@ege.edu.trIn this paper, we introduce $\beta$-paracompactness with respect to an ideal ($I$-$\beta$-paracompactness) as a weak form of $\beta$-paracompactness and $I$-paracompactness. We give some relations between this concept and some other types of paracompactness, and also we study some of its fundamental properties.2019-04-29T17:35:36+00:00Copyright (c) 2019 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3406Hankel Transform of (q,r)-Dowling Numbers2019-04-29T17:35:37+00:00Roberto B. Corcinomrlatayada@gmail.comMary Joy Regidor Latayadamrlatayada@gmail.comMary Ann Ritzell P. Vegamrlatayada@gmail.com<p>In this paper, we establish certain combinatorial interpretation for $q$-analogue of $r$-Whitney numbers of the second kind defined by Corcino and Ca\~{n}ete in the context of $A$-tableaux. We derive convolution-type identities by making use of the combinatorics of $A$-tableaux. Finally, we define a $q$-analogue of $r$-Dowling numbers and obtain some necessary properties including its Hankel transform.<br /><br /></p>2019-04-29T17:35:37+00:00Copyright (c) 2019 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3412Fuzzy Soft Sets over Fully UP-Semigroups2019-04-29T17:35:37+00:00Akarachai Satiradakarachai.sa@gmail.comAiyared Iampanaiyared.ia@up.ac.th<p>In this paper, we introduce ten types of fuzzy soft sets over fully UP-semigroups, and investigate the algebraic properties of fuzzy soft sets under the operations of (extended) intersection and (restricted) union.<br />Further, we discuss the relation between some conditions of fuzzy soft sets and fuzzy soft UP$\mathrm{_{s}}$-subalgebras (resp., fuzzy soft UP$\mathrm{_{i}}$-subalgebras, fuzzy soft near UP$\mathrm{_{s}}$-filters, fuzzy soft near UP$\mathrm{_{i}}$-filters, fuzzy soft UP$\mathrm{_{s}}$-filters, fuzzy soft UP$\mathrm{_{i}}$-filters, fuzzy soft UP$\mathrm{_{s}}$-ideals, fuzzy soft UP$\mathrm{_{i}}$-ideals, fuzzy soft strongly UP$\mathrm{_{s}}$-ideals, fuzzy soft strongly UP$\mathrm{_{i}}$-ideals) of fully UP-semigroups.</p>2019-04-29T17:35:37+00:00Copyright (c) 2019 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3380On Weak Graded Rings II2019-04-29T17:35:37+00:00Najla SH. Al-Subaienajlaa990@gmail.comMohammed Mosa Al-shomranimalshomrani@hotmail.com<p>The G-weak graded rings are rings graded by a set G of left coset representatives for the left action of a subgroup H of a finite group X. The main aim of this article is to study the concept of G-weak graded rings and continue the investigation of their properties. Moreover, some results concerning G-weak graded rings of fractions are derived. Finally, some additional examples of G-weak graded rings are provided.</p>2019-04-29T17:35:37+00:00Copyright (c) 2019 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3371Common Fixed Points of Two Multivalued Asymptotically Nonexpansive Mappings2019-04-29T17:35:37+00:00Safeer Hussain Khansafeerhussain5@yahoo.comHira Iqbalsafeerhussain5@yahoo.comMujahid Abbassafeerhussain5@yahoo.comIn this paper, we construct a modified Ishikawa iterative process to approximate common fixed points for two multivalued asymptotically nonexpansive mappings and prove some convergence theorems in uniformly convex hyperbolic spaces.2019-04-29T17:35:37+00:00Copyright (c) 2019 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3401On B-Open Sets2019-04-29T17:35:37+00:00Layth Muhsin Habeeb Alabdulsadalayth.muhsin@science.unideb.hu<p>The aim of this paper is to introduce and study $\mathcal{B}$-open sets and related properties. Also, we define a bi-operator topological space $(X, \tau, T_1, T_2)$, involving the two operators $T_1$ and $T_2$, which are used to define $\mathcal{B}$-open sets. A $\mathcal{B}$-open set is, roughly speaking, a generalization of a $b$-open set, which is, in turn, a generalization of a pre-open set and a semi-open set. We introduce a number of concepts based on $\mathcal{B}$-open sets.</p>2019-04-29T17:35:37+00:00Copyright (c) 2019 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3408Literature Survey on Non-Associative Rings and Developments2019-04-29T17:35:37+00:00Syed Tariq Shahstariqshah@gmail.comAsima Razzaqueasima.razzaque@yahoo.comInayatur Rehmanirehman@du.edu.omMuhammad Asif Gondalmgondal@du.edu.omMuhammad Iftikhar Farazfarazm@gvsu.eduKar Ping Shumkpshum@ynu.edu.cn<p>In this paper we present a comprehensive survey and developments of existing literature of non-associative rings and enumerate some of their various applications in different directions to date. These applications explain the voluminous work in different fields of non-associative rings and through which various algebraic structures in theoretical point of view could be developed.</p>2019-04-29T17:35:37+00:00Copyright (c) 2019 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3422Some Results on Fuzzy Implicative Hyper GR-ideals2019-04-29T17:35:37+00:00Amila Pagadilan Macodi-Ringiaamila.macodi-ringia@g.msuiit.edu.phGaudencio Petalcoringaudencio.petalcorin@g.msuiit.edu.ph<p>The implicative hyper GR-ideals, the fuzzy implicative hyper GR-ideals of type 1 and the fuzzy implicative hyper GR-ideals of type 2 are introduced, and several properties are investigated. Characterizations of fuzzy implicative hyper GR-ideals of type 1 are established using level subsets of fuzzy sets.</p>2019-04-29T17:35:37+00:00Copyright (c) 2019 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3391Convergence of β-Modified Jacobi-Perron Algorithm over the Field of Formal Power Series2019-04-29T17:35:37+00:00Amara Chandoulamarachandoul@yahoo.frFahad Aljuaydif.m.427@hotmail.comThe aim of this paper is to study multidimentional $\beta$-continued fraction algorithm over the field of formal power series. In the case of the Modified Jacobi-Perron algorithm, we prove that it converges.2019-04-29T17:35:37+00:00Copyright (c) 2019 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3407Monotone Iterative Technique and Ulam-Hyers Stability Analysis for Nonlinear Fractional Order Differential Equations with Integral Boundary Value Conditions2019-04-29T17:35:37+00:00Sajjad Alisajjad_ali@sbbu.edu.pkKamal Shahkamalshah408@gmail.comHassan Khanhassanmath@awkum.edu.pkMuhammad Arifmarifmaths@awkum.edu.pkShahid Mahmoodshahidmahmood757@gmail.comIn this manuscript, the monotone iterative scheme has been extended to the nature of solution to boundary value problem of fractional differential equation that consist integral boundary conditions. In this concern, some sufficient conditions are developed in this manuscript. On the base of sufficient conditions, the monotone iterative scheme combined with lower and upper solution method for the existence, uniqueness, error estimates and various view plots of the extremal solutions to boundary value problem of nonlinear fractional differential equations have been studied. The obtain results have clarified the nature of the extremal solutions. Further, the Ulam--Hyers and Ulam--Hyers--Rassias stability have been investigated for the considered problem. Two illustrative examples of the BVP of the nonlinear fractional differential equations have been provided to justify our contribution.2019-04-29T17:35:37+00:00Copyright (c) 2019 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3395Existence and Uniqueness Solution Under Non-Lipschiz Condition of the Mixed Fractional Heston's Model2019-04-29T17:35:37+00:00Didier Alain Njamen Njomendidiernjamen1@gmail.comEric Djeutchadidiernjamen1@gmail.comLouis-Aime Fonodidiernjamen1@gmail.comThis paper focuses on a mixed fractional version of Heston model in which the volatility Brownian and price Brownian are replaced by mixed fractional Brownian motion with the Hurst parameter $H\in(\frac{3}{4},1)$ so that the model exhibits the long range dependence. The existence and uniqueness of solution of mixed fractional Heston model is established under various non-Lipschitz condition and a related Euler discretization method is discussed. An example on the American put option price using Least Squares Monte Carlo Algorithm to produce acceptable results under the mixed fractional Heston model is presented to illustrate the applicability of the theory. The numerical result obtained proves the performance<br />of our results.2019-04-29T17:35:37+00:00Copyright (c) 2019 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3384The Quotient Inequalities2019-04-29T17:35:37+00:00Benedict Barnesewiekwamina@gmail.comC. Sebilewiekwamina@gmail.comI. K. Dontwiewiekwamina@gmail.comThis paper contributes to the inequalities, specifically, the relationships among the<br />norm of products of elements or vectors or functions and their quotients. Thus, we established that the norm of product of two vectors or functions is less than or equal to the norm of its quotient if the norm of the denominator is less than or equal to one. On the other hand, the norm of the quotient of two vectors or functions is less than or equal to the norm of their product is proved. In addition, we introduce the proofs of inequalities including the norm of index power of products and their quotients, and then applied these inequalities to estabish properties of some functional spaces, as well as, extend some of the results in these functional spaces.<br /><br />2019-04-29T17:35:37+00:00Copyright (c) 2019 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3373(p, q)-Growth of Entire Harmonic Functions in R^n in Terms of Approximation Errors2019-05-15T06:33:56+00:00Devendra Kumardkdev2013@gmail.comRifaqat Alirifaqat.ali1@gmail.com<p>The relationship between the generalized growth parameters of an entire harmonic<br />function in space Rn, n ≥ 3, with the rate of its best harmonic polynomial approximation error and ratios of these errors of functions harmonic in the ball of radius R has been studied.</p>2019-04-29T17:35:37+00:00Copyright (c) 2019 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3421On Topologies Induced by Graphs Under Some Unary and Binary Operations2019-04-29T17:35:37+00:00Caen Grace Sarona Niangacaengrace1997@gmail.comSergio R. Canoy Jr.caengrace1997@gmail.comLet G = (V (G),E(G)) be any simple undirected graph. The open hop neighborhood of v ϵ V(G) is the set 𝑁_𝐺^2(𝑣) = {u ϵ V(G): 𝑑_𝐺 (u,v) = 2}. Then G induces a topology τ_G on V (G) with base consisting of sets of the form F_G^2[A] = V(G) \ N_G^2 [A] where N_G^2 [A] = A ∪ {v ϵ V(G): 𝑁_𝐺^2(𝑣) ∩ A ≠ ∅ } and A ranges over all subsets of V (G). In this paper, we describe the topologies induced by the complement of a graph, the join, the corona, the composition and the Cartesian product of graphs.2019-04-29T17:35:37+00:00Copyright (c) 2019 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3416Optimal Control of a Time Delayed HIV-1 Infection Model2019-04-30T18:03:01+00:00Nigar Alinigaruom@gmail.comMuhammad Ikhlaq Chohannigaruom@gmail.comGul Zamannigaruom@gmail.comIn this paper, an optimal control problem of HIV infection model of delay differential equations is taken into account. Then we set a control function which represents the efficiency of reverse transcriptase inhibitors. Objective functional is constructed to minimize the virus concentration as well as treatment costs.Adjoint system is derived using Pontryagins Maximum Principle. Optimality system is calculated and numerical simulation is carried out to illustrate the theoretical results. Finally, conclusion is drawn2019-04-29T17:35:37+00:00Copyright (c) 2019 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3411General Solution of Linear Partial Differential Equations Modeling Homogeneous diffusion-convection-reaction Problems with Cauchy Initial Condition2019-04-29T17:35:37+00:00Minoungou Youssoufm.youl@yahoo.frBagayogo Moussamoussabagayogo94@gmail.comYoussouf Parepareyoussouf@yahoo.fr<p>In this paper, we propose the general solution of di¤usion-convection-<br />reaction homogeneous problems with condition initial of Cauchy, using the<br />SBA numerical method. This method is based on the combination of the<br />Adomian Decompositional Method(ADM), the successive approximations<br />method and the Picard principle.</p>2019-04-29T17:35:37+00:00Copyright (c) 2019 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3420Rough Spaces on Covering Based Rough Sets2019-04-29T17:35:38+00:00Nof Alharbinof20081900@hotmail.comHassen Aydihassen.aydi@isima.rnu.tnCenap Özelcenap.ozel@gmail.comIn this paper, we discuss open (closed) sets, rough interiors, rough closures, continuous mappings, open (closed) mappings and homeomorphism mappings of covering based rough topology of Akduman, Özcelik and Özel. We also construct the nano topology on a given covering based rough set.2019-04-29T17:35:38+00:00Copyright (c) 2019 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3397Weakly Prime and Weakly Primary Ideals in Gamma Seminearrings2019-04-29T17:35:38+00:00Waheed Ahmad Khansirwak2003@yahoo.comAbdelghani Taoutiganitaouti@yahoo.com.auSeema Karkainskarkain@hct.ac.aeAzar Salamiasalami@hct.ac.aeWaqar Arifwaqarvicky6699@gmail.comWe introduce and discuss the weakly prime and weakly primary ideals of a gamma<br />seminearrings with illustrative examples. We also present few of characterizations of these ideals.2019-04-29T17:35:38+00:00Copyright (c) 2019 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3418On Interval-Valued Fuzzy on Ideal Sets2019-04-29T17:35:38+00:00Mary Joy S. Togononmaryjoy.togonon@g.msuiit.edu.phRandy L. Caga-ananrandy.caga-anan@g.msuiit.edu.ph<p>Fuzzy sets, formalized by Zadeh in 1965, generalizes the classical idea of sets. The idea itself was generalized in 1975 when Zadeh introduced the interval-valued fuzzy sets. In this paper, we generalize further the above concepts by introducing interval-valued fuzzy on ideal sets, where an ideal is a nonempty collection of sets with a property describing the notion of smallness. We develop its basic concepts and properties and consider how one can create mappings of interval-valued fuzzy on ideal sets from mappings of ordinary sets. We then consider topology and continuity with respect to these sets.</p>2019-04-29T17:35:38+00:00Copyright (c) 2019 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3399Finite Groups with Certain Permutability Criteria2019-04-29T17:35:38+00:00Rola A. Hijazirhijazi@kau.edu.saFatme M. Charaffa-sharaf@hotmail.com<p>Let G be a finite group. A subgroup H of G is said to be S-permutable in G if it<br />permutes with all Sylow subgroups of G. In this note we prove that if P, the Sylow<br />p-subgroup of G (p > 2), has a subgroup D such that 1 <|D|<|P| and all subgroups H of P with |H| = |D| are S-permutable in G, then G′ is p-nilpotent.</p>2019-04-29T17:35:38+00:00Copyright (c) 2019 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3382On the Existence of Solution to Multidimensional Third Order Nonlinear Equations2019-04-29T17:35:38+00:00Samed Jahangir Aliyevsamed59@bk.ruArzu Q. Aliyevaarzu.aliyeva@bk.ruGoncha Z. Abdullayevaa.q.z.41@mail.ruIn this paper, we prove the existence of an almost everywhere solution to a mixed problem for a class of third order differential equations by non-zero rotation principle. Also studied the correctness of the formulation of the considered problem.2019-04-29T17:35:38+00:00Copyright (c) 2019 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3405On a Nonsingular Equation of Length 9 Over Torsion Free Groups2019-04-30T18:19:35+00:00M. Fazeel Anwarfazeel.anwar@iba-suk.edu.pkMairaj Bibimairaj_math@comsats.edu.pkMuhammad Saeed Akrammrsaeedakram@gmail.comIn \cite{levin}, Levin conjectured that every equation is solvable over a torsion free group. In this paper we consider a nonsingular equation $g_{1}tg_{2}t g_{3}t g_{4} t g_{5} t g_{6} t^{-1} g_{7} t g_{8}t \\ g_{9}t^{-1} = 1$ of length $9$ and show that it is solvable over torsion free groups modulo some exceptional cases.2019-04-29T17:35:38+00:00Copyright (c) 2019 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3403Combinatorial Identities with Generalized Higher-order Genocchi Sequences2019-04-29T17:35:38+00:00Tian Hao1179827028@qq.comWuyungaowa Baowuyungw@163.com<p>In this paper, we make use of the probabilistic method to calculate the moment representation of generalized higher-order Genocchi polynomials. We obtain the moment expression of the generalized higher-order Genocchi numbers with a and b parameters. Some characteriza tions and identities of generalized higher-order Genocchi polynomials are given by the proof of the moment expression. As far as properties given by predecessors are concerned, we prove them by the probabilistic method. Finally, new identities of relationships involving generalized higher-order Genocchi numbers and harmonic numbers, derangement numbers, Fibonacci numbers, Bell numbers, Bernoulli numbers, Euler numbers, Cauchy numbers and Stirling numbers of the second kind are established.</p><p> </p>2019-04-29T17:35:38+00:00Copyright (c) 2019 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3427Direct Product of Finite Intuitionistic Anti Fuzzy Normal Subrings over Non-associative Rings2019-04-29T17:35:38+00:00Nasreen Kausarkausar.nasreen57@gmail.comShal et. al cite:SKR, have introduced the concept of intuitionistic fuzzy normal subrings over a non-associative ring. In this paper, we investigate the concept of intuitionistic anti fuzzy normal subrings over non-associative rings and give some properties of such subrings2019-04-29T17:35:38+00:00Copyright (c) 2019 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3372Some Estimates Below the Modulus of Integrals of Some Polynomials in the Complex Plane2019-04-29T17:35:38+00:00Todor Stoyanov Stoyanovtodstoyanov@yahoo.com<p>In this paper, we make some estimates below the modulus of some integrals in the<br />complex plane. Our aim is to prove the Conjecture1, which we could see in [2–4]. The proof of the conjecture appears the Corollary.</p>2019-04-29T17:35:38+00:00Copyright (c) 2019 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3375A differential Game Related to Terrorism: Stackelberg Differential Game of E-differentiable and E-convex Function2019-05-19T08:51:13+00:00Abd El-Monem Megaheda_megahed15@yahoo.com<p>In this work, the Stackelberg differential game of $E$-differentiable and $E$ convex function is studied in order to fight the terrorism taking into account the government's procedures such as education quality, better job opportunity, social justice, religious awareness and security arrangements. We consider Stackelberg differential game. Firstly, the government is the leader and the terrorist organization is the follower. Secondly, the terrorist organization is the leader and the government is a follower. Furthermore, we apply the necessary conditions of the Stackelberg differential game for these cases to obtain the optimal strategy of this problem.</p>2019-04-29T17:35:38+00:00Copyright (c) 2019 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3419Counting Z2 Z4 Z8-additive Codes2019-04-29T17:35:38+00:00Basri Çalışkanbcaliskan@osmaniye.edu.trKemal Balıkçıkbalikci@osmaniye.edu.trIn Algebraic Coding Theory, all linear codes are described by generator matrices. Any linear code has many generator matrices which are equivalent. It is important to find the number of the generator matrices for constructing of these codes. In this paper, we study Z_2 Z_4 Z_8-additive codes, which are the extension of recently introduced Z_2 Z_4-additive codes. We count the number of arbitrary Z_2 Z_4 Z_8-additive codes. Then we investigate connections to Z_2 Z_4 and Z_2 Z_8-additive codes with Z_2 Z_4 Z_8, and give some illustrative examples.2019-04-29T17:35:38+00:00Copyright (c) 2019 European Journal of Pure and Applied Mathematics