European Journal of Pure and Applied Mathematics
https://ejpam.com/index.php/ejpam
<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>en-USEuropean Journal of Pure and Applied Mathematics1307-5543<p align="justify">Upon acceptance of an article by the journal, the author(s) accept(s) the transfer of copyright of the article to <em>European Journal of Pure and Applied Mathematics. </em></p><p align="justify"><em>European Journal of Pure and Applied Mathematics will be Copyrihgt Holder.</em></p><p align="justify">If necessary, authors are responsible for obtaining permissions to reprint previously published figures, tables, and other material.</p>Correction to the Article: "An Introduction to the Theory of Hyperlattices"
https://ejpam.com/index.php/ejpam/article/view/3415
The 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.Niovi Kehayopulu
Copyright (c) 2019 European Journal of Pure and Applied Mathematics
2019-04-292019-04-2912225226910.29020/nybg.ejpam.v12i2.3415Some Characterizations of β-paracompactness in Ideal Topological Space
https://ejpam.com/index.php/ejpam/article/view/3394
In 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.Esra Dalan YıldırımOya Bedre ÖzbakırAysegul Caksu Guler
Copyright (c) 2019 European Journal of Pure and Applied Mathematics
2019-04-292019-04-2912227027810.29020/nybg.ejpam.v12i2.3394Hankel Transform of (q,r)-Dowling Numbers
https://ejpam.com/index.php/ejpam/article/view/3406
<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>Roberto B. CorcinoMary Joy Regidor LatayadaMary Ann Ritzell P. Vega
Copyright (c) 2019 European Journal of Pure and Applied Mathematics
2019-04-292019-04-2912227929310.29020/nybg.ejpam.v12i2.3406Fuzzy Soft Sets over Fully UP-Semigroups
https://ejpam.com/index.php/ejpam/article/view/3412
<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>Akarachai SatiradAiyared Iampan
Copyright (c) 2019 European Journal of Pure and Applied Mathematics
2019-04-292019-04-2912229433110.29020/nybg.ejpam.v12i2.3412On Weak Graded Rings II
https://ejpam.com/index.php/ejpam/article/view/3380
<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>Najla SH. Al-SubaieMohammed Mosa Al-shomrani
Copyright (c) 2019 European Journal of Pure and Applied Mathematics
2019-04-292019-04-2912233234710.29020/nybg.ejpam.v12i2.3380Common Fixed Points of Two Multivalued Asymptotically Nonexpansive Mappings
https://ejpam.com/index.php/ejpam/article/view/3371
In 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.Safeer Hussain KhanHira IqbalMujahid Abbas
Copyright (c) 2019 European Journal of Pure and Applied Mathematics
2019-04-292019-04-2912234835710.29020/nybg.ejpam.v12i2.3371On B-Open Sets
https://ejpam.com/index.php/ejpam/article/view/3401
<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>Layth Muhsin Habeeb Alabdulsada
Copyright (c) 2019 European Journal of Pure and Applied Mathematics
2019-04-292019-04-2912235836910.29020/nybg.ejpam.v12i2.3401Literature Survey on Non-Associative Rings and Developments
https://ejpam.com/index.php/ejpam/article/view/3408
<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>Syed Tariq ShahAsima RazzaqueInayatur RehmanMuhammad Asif GondalMuhammad Iftikhar FarazKar Ping Shum
Copyright (c) 2019 European Journal of Pure and Applied Mathematics
2019-04-292019-04-2912237040810.29020/nybg.ejpam.v12i2.3408Some Results on Fuzzy Implicative Hyper GR-ideals
https://ejpam.com/index.php/ejpam/article/view/3422
<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>Amila Pagadilan Macodi-RingiaGaudencio Petalcorin
Copyright (c) 2019 European Journal of Pure and Applied Mathematics
2019-04-292019-04-2912240941710.29020/nybg.ejpam.v12i2.3422Convergence of β-Modified Jacobi-Perron Algorithm over the Field of Formal Power Series
https://ejpam.com/index.php/ejpam/article/view/3391
The 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.Amara ChandoulFahad Aljuaydi
Copyright (c) 2019 European Journal of Pure and Applied Mathematics
2019-04-292019-04-2912241843110.29020/nybg.ejpam.v12i2.3391Monotone Iterative Technique and Ulam-Hyers Stability Analysis for Nonlinear Fractional Order Differential Equations with Integral Boundary Value Conditions
https://ejpam.com/index.php/ejpam/article/view/3407
In 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.Sajjad AliKamal ShahHassan KhanMuhammad ArifShahid Mahmood
Copyright (c) 2019 European Journal of Pure and Applied Mathematics
2019-04-292019-04-2912243244710.29020/nybg.ejpam.v12i2.3407Existence and Uniqueness Solution Under Non-Lipschiz Condition of the Mixed Fractional Heston's Model
https://ejpam.com/index.php/ejpam/article/view/3395
This 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.Didier Alain Njamen NjomenEric DjeutchaLouis-Aime Fono
Copyright (c) 2019 European Journal of Pure and Applied Mathematics
2019-04-292019-04-2912244846810.29020/nybg.ejpam.v12i2.3395The Quotient Inequalities
https://ejpam.com/index.php/ejpam/article/view/3384
This 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 />Benedict BarnesC. SebilI. K. Dontwi
Copyright (c) 2019 European Journal of Pure and Applied Mathematics
2019-04-292019-04-2912246948510.29020/nybg.ejpam.v12i2.3384(p, q)-Growth of Entire Harmonic Functions in R^n in Terms of Approximation Errors
https://ejpam.com/index.php/ejpam/article/view/3373
<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>Devendra KumarRifaqat Ali
Copyright (c) 2019 European Journal of Pure and Applied Mathematics
2019-04-292019-04-2912248649810.29020/nybg.ejpam.v12i2.3373On Topologies Induced by Graphs Under Some Unary and Binary Operations
https://ejpam.com/index.php/ejpam/article/view/3421
Let 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.Caen Grace Sarona NiangaSergio R. Canoy Jr.
Copyright (c) 2019 European Journal of Pure and Applied Mathematics
2019-04-292019-04-2912249950510.29020/nybg.ejpam.v12i2.3421Optimal Control of a Time Delayed HIV-1 Infection Model
https://ejpam.com/index.php/ejpam/article/view/3416
In 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 drawnNigar AliMuhammad Ikhlaq ChohanGul Zaman
Copyright (c) 2019 European Journal of Pure and Applied Mathematics
2019-04-292019-04-2912250651810.29020/nybg.ejpam.v12i2.3416General Solution of Linear Partial Differential Equations Modeling Homogeneous diffusion-convection-reaction Problems with Cauchy Initial Condition
https://ejpam.com/index.php/ejpam/article/view/3411
<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>Minoungou YoussoufBagayogo MoussaYoussouf Pare
Copyright (c) 2019 European Journal of Pure and Applied Mathematics
2019-04-292019-04-2912251953210.29020/nybg.ejpam.v12i2.3411Rough Spaces on Covering Based Rough Sets
https://ejpam.com/index.php/ejpam/article/view/3420
In 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.Nof AlharbiHassen AydiCenap Özel
Copyright (c) 2019 European Journal of Pure and Applied Mathematics
2019-04-292019-04-2912253354310.29020/nybg.ejpam.v12i2.3420Weakly Prime and Weakly Primary Ideals in Gamma Seminearrings
https://ejpam.com/index.php/ejpam/article/view/3397
We 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.Waheed Ahmad KhanAbdelghani TaoutiSeema KarkainAzar SalamiWaqar Arif
Copyright (c) 2019 European Journal of Pure and Applied Mathematics
2019-04-292019-04-2912254455210.29020/nybg.ejpam.v12i2.3397On Interval-Valued Fuzzy on Ideal Sets
https://ejpam.com/index.php/ejpam/article/view/3418
<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>Mary Joy S. TogononRandy L. Caga-anan
Copyright (c) 2019 European Journal of Pure and Applied Mathematics
2019-04-292019-04-2912255357010.29020/nybg.ejpam.v12i2.3418Finite Groups with Certain Permutability Criteria
https://ejpam.com/index.php/ejpam/article/view/3399
<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>Rola A. HijaziFatme M. Charaf
Copyright (c) 2019 European Journal of Pure and Applied Mathematics
2019-04-292019-04-2912257157610.29020/nybg.ejpam.v12i2.3399On the Existence of Solution to Multidimensional Third Order Nonlinear Equations
https://ejpam.com/index.php/ejpam/article/view/3382
In 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.Samed Jahangir AliyevArzu Q. AliyevaGoncha Z. Abdullayeva
Copyright (c) 2019 European Journal of Pure and Applied Mathematics
2019-04-292019-04-2912257758910.29020/nybg.ejpam.v12i2.3382On a Nonsingular Equation of Length 9 Over Torsion Free Groups
https://ejpam.com/index.php/ejpam/article/view/3405
In \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.M. Fazeel AnwarMairaj BibiMuhammad Saeed Akram
Copyright (c) 2019 European Journal of Pure and Applied Mathematics
2019-04-292019-04-2912259060410.29020/nybg.ejpam.v12i2.3405Combinatorial Identities with Generalized Higher-order Genocchi Sequences
https://ejpam.com/index.php/ejpam/article/view/3403
<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>Tian HaoWuyungaowa Bao
Copyright (c) 2019 European Journal of Pure and Applied Mathematics
2019-04-292019-04-2912260562110.29020/nybg.ejpam.v12i2.3403Direct Product of Finite Intuitionistic Anti Fuzzy Normal Subrings over Non-associative Rings
https://ejpam.com/index.php/ejpam/article/view/3427
Shal 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 subringsNasreen Kausar
Copyright (c) 2019 European Journal of Pure and Applied Mathematics
2019-04-292019-04-2912262264810.29020/nybg.ejpam.v12i2.3427Some Estimates Below the Modulus of Integrals of Some Polynomials in the Complex Plane
https://ejpam.com/index.php/ejpam/article/view/3372
<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>Todor Stoyanov Stoyanov
Copyright (c) 2019 European Journal of Pure and Applied Mathematics
2019-04-292019-04-2912264965310.29020/nybg.ejpam.v12i2.3372A differential Game Related to Terrorism: Stackelberg Differential Game of E-differentiable and E-convex Function
https://ejpam.com/index.php/ejpam/article/view/3375
<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>Abd El-Monem Megahed
Copyright (c) 2019 European Journal of Pure and Applied Mathematics
2019-04-292019-04-2912265466710.29020/nybg.ejpam.v12i2.3375Counting Z2 Z4 Z8-additive Codes
https://ejpam.com/index.php/ejpam/article/view/3419
In 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.Basri ÇalışkanKemal Balıkçı
Copyright (c) 2019 European Journal of Pure and Applied Mathematics
2019-04-292019-04-2912266867910.29020/nybg.ejpam.v12i2.3419