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Latest Issue

Volume 14, No. 3, September 2021




Patterns of Time Scale Dynamic Inequalities Settled by Kantorovich's Ratio

In this research article, we present an interesting generalization of dynamic Kantorovich’s inequality and investigate the additive versions of some dynamic inequalities on time scales. The time scale dynamic inequalities extend and unify some continuous inequalities and their corresponding discrete versions.


Muhammad Jibril Shahab Sahir



JJMS, 2021, 14(3), 397-410


In this paper, we introduce the notion of (s, p)-convex functions and establish an integral equality and some Hermite-Hadamard type integral inequalities of (s, p)-convex functions in fractional form. Also give some Hermite-Hadamard type integral inequalities of product of two (s, p)-convex functions in fractional form.


N. Mehreen
M. Anwar



JJMS, 2021, 14(3), 411-435


Common Fixed Point for A Sequence of Multivalued (G, Θ)-Prešić Type Maps in Symmetric Spaces Endowed with a Graph

We have obtained some new common fixed point results for a sequence of multivalued (G, θ)-Prešić type mappings in a symmetric space equipped with a graph. An example of application is provided. Some results from the literature are extended or improved.


Saadia Benchabane
Smaïl Djebali

JJMS, 2021, 14(3), 437-452


Solving the Optimal Control of Volterra-Fredholm integro-differential equation via Müntz polynomials

The main goal of the current paper is to present a direct numerical method for solving optimal control problem for systems governed by Volterra-Fredholm integro-differential equation. This method is based upon a new form of orthogonal Müntz-Legendre polynomials, and collocation method to transform the optimal control problem to a nonlinear programming problem with finite-dimensional.
The accuracy and efficiency of the proposed method are examined with illustrative examples.



Neda Negarchi
Sayyed Yaghoub Zolfegharifar


JJMS, 2021, 14(3), 453-466


A Generalization of Jacobsthal and Jacobsthal-Lucas Numbers

In this paper, we study a generalization of Jacobsthal and Jacobsthal-Lucas numbers. We describe their distinct properties also we give the related matrix representation and sum of terms of the sequences.


Ala’a Al-Kateeb




JJMS, 2021, 14(3), 467-481


The Connected Restrained Edge Monophonic Number of a Graph

For a connected graph G = (V, E) of order at least two, a connected restrained edge monophonic set of a graph G is a restrained edge monophonic set S such that the subgraph G[S] induced by S is connected. The minimum cardinality of a connected restrained edge monophonic set of G is the connected restrained edge monophonic number of G and is denoted by emcr(G). We determine bounds for it and some general properties satisfied by this parameter are studied. For every pair a, b of positive integers with 4 ≤ a ≤ b, there is a connected graph G such that emr(G) = a and emcr(G) = b, where emr(G) is the restrained edge monophonic number of G. Also, if n, d and k are positive integers such that 4 ≤ d ≤ n − 2, k ≥ 4 and n − d − k + 2 ≥ 0, then there exists a connected graph G of order n, monophonic diameter d and emcr(G) = k.


A. P. Santhakumaran
T. Venkata Raghu
K. Ganesamoorthy



JJMS, 2021, 14(3), 483-492


On Nearly Compact Spaces via Pre-Open Sets

Recently, the first author of this paper in a collaborative research work redefined the concept of nearly compact spaces by pre-open sets and obtained some new properties on nearly compact spaces when they are studied from this new perspective. In this paper, we continue to study the idea of near compactness via pre-open sets and obtain some new characterizations on nearly compact spaces.



Ajoy Mukharjee
Pratap Kumar Saha




JJMS, 2021, 14(3), 493-503



On Commuting Graphs Associated to BCI-Algebras

In this paper, first, the graph Γ(X) associated to a BCI-algebra X is studied and some related properties are established. Especially, a necessary and sufficient condition for Γ(X) to be a complete graph is given. After that, the commuting graph associated to a BCI-algebra X, denoted by G(X), is defined and some related properties are investigated. The paper provides a necessary and sufficient condition for the p-semisimple part of X to be an ideal. Moreover, a condition for an element of a BCI-algebra X to be minimal is given. Finally, it is proved that a BCI-algebra X is p-semisimple if and only if G(X) is a complete graph.


H. Harizavi


JJMS, 2021, 14(3), 505-516



The Theta-Complete Graph Ramsey Number
R(θn, K7); n = 7; n ≥ 14.

The Ramsey theory is an important branch in graph Theory. Finding the Ramsey number is an important topic in the Ramsey theory. The Ramsey number R(G, H) is the smallest positive integer n such that any graph of order n contains the graph G or its complement contains the graph H. In this paper, we prove that R(θn, K7) = 6(n − 1) + 1, n = 7; n ≥ 14, where θn is a theta graph of order n and K7 is the complete graph of order 7.



A. Baniabedalruhman



JJMS, 2021, 14(3), 517-526



Pompeiu Type Inequalities using Conformable Fractional Calculus and its Applications

We establish Pompeiu’s mean value theorem for α-fractional differentiable mappings. Then, some Pompeiu type inequalities including conformable fractional integrals are obtained, and the weighted versions of this Pompeiu type in equalities are presented. Finally, some applications for quadrature rules and special means are given.

  Samet Erden
M. Zeki Sarikaya



JJMS, 2021, 14(3), 527-544


Sum 2-Irreducible Submodules of a Module

Let R be a commutative ring with identity and M be an R-module. M is said to be sum-irreducible precisely when it is non-zero and cannot be expressed as the sum of two proper submodules of itself. In this paper, we will introduce the concept of sum 2-irreducible submodules of M as a generalization of sum irreducible submodules of M and investigate some basic properties of this class of modules.

  F. Farshadifar
H. Ansari-Toroghy



JJMS, 2021, 14(3), 545-554


CAS Wavelets Stochastic Operational Matrix of Integration and its Application for Solving Stochastic Itô-Volterra Integral Equations

This article provides an effective technique for solving stochastic Itô-Volterra integral equations using Cosine and Sine (CAS) wavelets. A novel stochastic operational matrix of integration of CAS wavelets is developed in this article for solving stochastic Itô-Volterra integral equations. Stochastic Itô-Volterra integral equation can be reduced to a system of algebraic equations using the newly generated stochastic operational matrix of integration of CAS wavelets along with the operational matrix of integration of CAS wavelets. These system of algebraic equations can be solved using appropriate methods. Convergence and the error analysis of the proposed technique is studied in detail. Numerical examples are presented in order to show the efficiency and reliability of the proposed method.

  S. C. Shiralashetti
Lata Lamani



JJMS, 2021, 14(3), 555-580