Articles

An Efficient Haar Wavelet Series Method to Solve
Higher-order Multi-pantograph Equations Arising
in Electrodynamics

The primary aim of this paper is to develop a numerical method based
on Haar wavelets for solving second and higher-order multi-pantograph differential equations. This method transforms the differential equation into a system of algebraic equations with undetermined coefficients. These algebraic systems can be solved either by Newton’s or Broyden’s iterative methods. Finally, few test examples are taken from the literature to show the computational efficiency of this method.

Akhilesh Yadav
Sachin Kumar




 

JJMS, 2022, 15(4A), 823-841

Suroto
Diah Junia Eksi Palupi
Ari Suparwanto





 

Khaled M. Hyasat
Maher Nazmi Qarawani



 

JJMS, 2022, 15(4A), 857-870

H. Özlem Güney
Shigeyoshi Owa




 

JJMS, 2022, 15(4A), 871-894

Analytic Properties of the Apostol-Vu Multiple Lucas L-functions

In the article we study the analytic continuations of the Apostol-Vu multiple shifted Lucas zeta functions and Apostol-Vu multiple Lucas L-functions associated to Dirichlet characters. We also compute a complete list of exact singularities and residues of these functions at poles.

Utkal Keshari Dutta
Prasanta Kumar Ray

 

JJMS, 2022, 15(4A), 895-909

K-Product Cordial Labeling of Powers of Paths

Let f be a map from V (G) to {0, 1, ..., k − 1}, where k is an integer and 1 ≤ k ≤ |V (G)|. For each edge uv assign the label f(u)f(v)(mod k). f is called a k-product cordial labeling if |v_f (i) − v_f (j)| ≤ 1, and |e_f (i) − e_f (j)| ≤ 1, i, j ϵ {0, 1, ..., k − 1}, where v_f (x) and e_f (x) denote the number of vertices and edges, respectively labeled with x (x = 0, 1, ..., k − 1). In this paper, we add some new results on k-product cordial labeling and prove that the graph P²_n is 4-product cordial. Further, we study the k-product cordial behaviour of powers of paths
P³_n, P⁴_n and P⁵_n for k = 3 and 4.

K. Jeya Daisy
R. Santrin Sabibha
P. Jeyanthi
Maged Z. Youssef



 

JJMS, 2022, 15(4A), 911-924

Vague Modules on the Base of ([0, 1], ≤, ∧)

In this paper, the concepts of vague module, vague submodule, vague module homomorphism and vague module isomorphism based on the Demirci’s vague groups are defined. Then various elementary properties of these concepts are obtained, and the validity of some relevant classical results in these settings are investigated.

Sevda Sezer
Murat Yüksel


 

JJMS, 2022, 15(4A), 925-939

Periodic Oscillation of the Solutions for a Model of Four-Disk Dynamo System with Delays

In this paper, the periodic oscillatory behavior of the solutions for a model of four-disk dynamo system with delays is investigated. By means of the mathematical analysis method, some sufficient conditions to guarantee the periodic oscillation of the solutions are obtained. Computer simulations are provided to demonstrate our results.

Chunhua Feng

 

JJMS, 2022, 15(4A), 941-953

Class of Analytic Univalent Functions with Fixed Finite Negative Coefficients Defined by q-Analogue Difference Operator

In this paper using a q−analogue operator, we define class of univalent functions with fixed finite negative coefficients and determine coefficient estimates and other properties for this class. Various results obtained in this paper are shown to be sharp. 

Z. M. Saleh

A. O. Mostafa

 

JJMS, 2022, 15(4A), 955-965

Further Results on I and I*−Convergence of Sequences in Gradual Normed Linear Spaces

In this paper, following a very recent and new approach, we introduce the notion of gradual I−limit point, gradual I−cluster point, and prove certain properties of both the notions. We also investigate some new properties of gradual I−Cauchy and gradual I*−Cauchy sequences and show that the condition (AP) plays a crucial role to relate both the notions. Finally, we investigate the notion of I and I*−divergence of sequences in gradual normed linear spaces and prove the essence of the condition (AP) again to establish the relationship between the notions.

Chiranjib Choudhury
Shyamal Debnath


 

JJMS, 2022, 15(4A), 967-982

Existence and Uniqueness of Weak Solution for Nonlinear Weighted (p; q)-Laplacian System with Application on an Optimal Control Problem

In this paper, we prove the existence and uniqueness results of weak solution for weighted (p, q)-Laplacian system with Dirichlet boundary condition.
The proof of the results is made by Browder theorem method. Also, the optimal control of the weighted (p, q)-Laplacian system will be study as an application.

Salah A. Khafagy
Eada. A. El-Zahrani
Hassan M. Serag



 

JJMS, 2022, 15(4A), 983-998

In this paper, we establish the existence and uniqueness of solutions for
a class of problem for nonlinear implicit fractional differential equations of Caputo-Hadamard type with fractional boundary conditions. The results are obtained by using Banach fixed point theorem and Schauder’s fixed point theorem. An example is included to show the applicability of our results.

JJMS, 2022, 15(4B), 999-1014

A commutative ring R with unity is called weakly-présimplifiable (resp., présimplifiable) if for a, b ϵ R with a = ba, then either a = 0 or b is a regular element (that is, b is not a zero-divisor) in R (resp., a = 0 or b is a unit in R). Let R be a commutative ring with unity and G be a nontrivial abelian group. In this paper, we give some characterizations for the group ring R[G] to be weakly présimplifiable.
Furthermore, we give a complete description of (weakly) présimplifiable circulant matrix ring.

JJMS, 2022, 15(4B), 1015-1029

We are introducing very first time a generalized class named it the class of (s, r)−convex functions in mixed kind. This generalized class contains many subclasses including class of s−convex functions in 1^st and 2^nd kind, P−convex functions, quasi convex functions and the class of ordinary convex functions. Also, we would like to state the generalization of the classical Ostrowski inequality via fractional integrals, which is obtained for functions whose first derivative in absolute values is (s, r)− convex function in mixed kind. Moreover we establish some Ostrowski type inequalities via fractional integrals and their particular cases for the class of functions whose absolute values at certain powers of derivatives are (s, r)−convex functions in mixed kind by using different techniques including Hölder’s inequality and power mean inequality. Also, various established results would be captured as special cases. Moreover, some applications in terms of special means would also be given.

JJMS, 2022, 15(4B), 1031-1047

The notion of stability of functional equations was posed by Ulam, and then, Hyers gave the first significant partial solution. This type of stability has been established and developed by an increasing number of mathematicians in various spaces. In Lipschitz spaces, the notion of stability was introduced by Tabor and Czerwik. This notion has been considered less attention over the recent years in Lipschitz spaces. In this paper, we consider this type of stability and we prove the stability of the generalized quadratic functional equations of three variables in
Lipschitz spaces. We generalize the stability of a quadratic functional equation from a special case to a general case and improve its approximation announced by Czerwik et al. in [4].

JJMS, 2022, 15(4B), 1049-1063

In this paper, we get a closer view to sub-chaotic C0-semigroups. We show that if a C₀-semigroup contains a subspace-chaotic operator, then it is sub-chaotic. We prove that there are sub-chaotic C₀-semigroups that contain no subspace-chaotic operator. We also prove that if φ is a bounded and holomorphic function on the unit disk, then the multiplication C₀-semigroup generated by φ can not be sub-chaotic. Moreover, we state some criteria for a C₀-semigroup to be sub-chaotic based on the properties of the operators that made the semigroup.

JJMS, 2022, 15(4B), 1065-1076

In this paper, we used the result that complex hyperbolic spaces CH²
(−4c/3) with holomorphic sectional curvature −4c/3 are isometrically embedded in E⁸₄ . By considering a circle in CH²(−4c/3), we prove that the image of the circle by isometric embedding is a proper helix of order 6 in E⁸₄. Moreover, we define a generalized LC helix on a submanifold of E⁸₄. Also, we show that the image of a circle by isometric embedding from complex hyperbolic plane CH²(−4c/3) to pseudo-Euclidean space E⁸₄ is a generalized LC helix on some submanifold of E⁸₄

JJMS, 2022, 15(4B), 1077-1092

We introduce the notion of quasi bi-slant submanifolds of nearly Kaehler manifolds and study some of thier properties. The necessary and sufficient conditions for the integrability of distributions, involved in the definition of quasi bi-slant submanifolds of nearly Kaehler manifolds, are obtained. We also investigate the necessary and sufficient conditions for quasi bi-slant submanifolds of nearly Kaehler manifolds to be totally geodesic, and we study the geometry of foliations. Finally, we construct some non-trivial examples of quasi bi-slant manifolds of nearly Kaehler manifolds.

JJMS, 2022, 15(4B), 1093-1110

Motivated with the study of discrete weaving frames by Bemrose et al. in 2015, we study generalized continuous K-weaving frames in Hilbert spaces and prove some new basic properties. Also, we prove a sufficient condition for generalized continuous K-frame to be woven. Further, we prove that generalized continuous K-weaving frames remain woven under invertible operator. Finally, we give Paley-Wiener type perturbation results for generalized continuous K-weaving
frames.

JJMS, 2022, 15(4B), 1111-1126

Establishing the lower and upper bound estimates for the maximum modulus of the derivative of composition of polynomials p(q(z)), where q(z) is a polynomial of degree m is an intriguing problem in geometric theory of polynomials.
In this paper, the maximum modulus for composite polynomials of Bernstein type is taken up with constraints such as the given polynomial does not vanish in the disc |z| < k, where k ≥ 1 which in particular yields some known inequalities of this type as special cases. In addition, the case when all the zeros of the underlying polynomial lie in |z| ≤ k, where k ≤ 1 is also considered.

JJMS, 2022, 15(4B), 1127-1135

The Matusita overlapping coefficient ρ is defined as agreement or similarity between two or more distributions. The parametric normal distribution is one of the most important statistical distributions. Under the assumption that the data at hand follow two independent normal distributions, this paper suggests a new technique to estimate the Matusita coefficient ρ. In contrast to the studies in the literature, the suggested technique requires no assumptions on the location and scale parameters of the normal distributions. The finite properties of the resulting estimators are investigated and compared with the nonparametric kernel estimators and with some existing estimators via simulation techniques. The results show that the performance of the proposed estimators is better than the kernel estimators for all considered cases.

JJMS, 2022, 15(4B), 1137-1151

The notions of GE-filter expansion and ξ-primary GE-filter are introduced and their properties are investigated. Different ways to create a GE-filter expansion are provided. The notion of good GE-filter expansion is introduced and its properties investigated. The conditions for an image and an inverse image of a ξ-primary GE-filter of a GE-algebra to be a ξ-primary GE-filter are provided.

JJMS, 2022, 15(4B), 1153-1171

The stable and unstable sets or stable and unstable manifolds give a formal mathematical definition to the general notions embodied in the idea of an attractor. In this paper, we will determine the stable and unstable manifolds of the normal form of two-dimensional piecewise-linear maps in the neighborhood of a fixed point at the border using stable manifold theorem, this is an important result about the structure of the set of orbits approaching to a hyperbolic fixed point.

JJMS, 2022, 15(4B), 1173-1192