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Latest Issue

Volume 16, No. 4, December 2023

A Novel Fixed Point Theorem of Reich-Perov Type α−Contractive Mapping in Vector-Valued Metric Spaces

This article discusses a novel concept of Reich-Perov type α-contractive mappings in vector-valued metric spaces. First, we define Reich-Perov-type contractive mappings using a novel concept in vector-valued metric spaces. Later, we investigate the sufficient conditions for a Reich-Perov type contractive mapping to have a unique fixed point in the spaces. By defining an α-contractive mapping, we next show the sufficient conditions of the existence and uniqueness of a fixed point of the Reich-Perov type α-contractive mappings in vector-valued metric spaces.

 

Sunarsini
Mahmud Yunus
Subiono



 

 

JJMS, 2023, 16(4), 599-616

This article investigates into the study of nonlinear hybrid fractional boundary value problems, which involve ϕ-Caputo derivatives of fractional order and two-point hybrid boundary conditions. The author utilizes a fixed point theorem of Dhage to provide evidence for the existence and uniqueness of solutions, taking into consideration mixed Lipschitz and Caratheodory conditions. Additionally, the Ulam-Hyers types of stability are established in this context. The article concludes by introducing a class of fractional boundary value problems, which are dependent on the arbitrary values of ϕ and the boundary conditions chosen. The research presented in this article has the potential to be useful in various fields, such as engineering and science, where fractional differential equations are frequently used to model complex phenomena.

 

Yahia Awad


 

JJMS, 2023, 16(4), 617-647

Two-Dimensional Quaternionic Fractional Mellin Transform of a Particular Order

Author introduces two-dimensional quaternionic fractional Mellin trans form defined for a particular order α, β of integrable functions on R2 and prove its inversion formula using the relation between fractional Fourier transform and fractional Mellin transform. Properties like linearity, Parseval’s formula and product theorem are obtained without any additional conditions. Applications of two dimensional quaternionic fractional Mellin transform are given to support the study.

 

Khinal Parmar
V. R. Lakshmi Gorty



 


JJMS, 2023, 16(4), 649-668

Closed Balls Included in the Inverted Multibrot and Multicorn Sets

The aim of this article is to compute a radius of a closed ball included in the Inverted Multibrot and Multicorn sets. More exactly, for w ϵ C*
a complex solution of the equation zk−1 = −1 we compute r > 0 such that............................

 

Dan Dumitru




 

JJMS, 2023, 16(4), 669-680

New Notions of Rough Statistical Convergence of Triple Sequences in Gradual Normed Linear Spaces

In the present article, we introduce and investigate the concept of statistical convergence for triple sequences in gradual normed linear spaces. We prove some of its fundamental properties and a few implication relations. We then concentrate on rough statistical convergence for triple sequences in gradual normed linear spaces and established some of its features based............................

 

 

Ӧmer Kişi
Chiranjib Choudhury




 

JJMS, 2023, 16(4), 681-702

The Cycle-Complete Graph Ramsey Numbers
R(Cn, K8), For 10 ≤ n ≤ 15

Given two graphs H1 and H2, the Ramsey number R(H1, H2) is the smallest natural number n such that each graph of order n contains a copy of H1 or its complement contains a copy of H2. In this paper, we find the exact Ramsey number R(Cn, K8) for 10 ≤ n ≤ 15, where Cn is the cycle on n vertices and K8 is the complete graph of order 8.

 

A. Baniabedalruhman




 

JJMS, 2023, 16(4), 703-718

A New Cubic Transmuted Power Function Distribution: Properties, Inference and Application

A new cubic transmuted power function distribution has been proposed by using the cubic transmuted family of distributions, proposed by [1]. The proposed distribution provides transmuted power function distribution as a special case. The properties of the proposed distribution are studied that include shape, moments, quantiles, entropy, random number generation and order statistics. The maximum likelihood estimation of the parameters of the proposed distribution is discussed. A simulation study has been conducted to observe the performance of the estimation procedure. The proposed distribution has been applied to real data sets to compare the suitability of the model.

 

Mariyam Hafeez
Rashida Khalil
Naila Amjad



 

 

JJMS, 2023, 16(4), 719-739

Estimation of Overlapping Measures using Numerical Approximations: Weibull Distributions

This paper deals with the estimation problem of the two overlapping (OVL) measures, namely; Matusita ρ and Morisita λ measures when two independent random variables X and Y follow Weibull distribution. The two measures ρ and λ have been studied in the literature in the case of two Weibull distributions under the assumption that the two shape parameters are equal. In this work, a new general expression for each measure is provided under the Weibull distribution without using any assumptions about the distribution parameters. The numerical integration methods known as trapezoidal, Simpson 1/3 and Simpson 3/8 rules that facilitate making inference on these measures are utilized. The relative bias (RB) and relative mean square error (RMSE) of the resulting proposed estimators were investigated and compared with some existing estimators via Monte-Carlo simulation technique. The results demonstrated clearly the superiority of the proposed estimators over the existing one in almost all considered cases.

 

Omar M. Eidous
Mervat M. Abu Al-Hayja`a



 

 

JJMS, 2023, 16(4), 741-761

Homotopy Analysis Method for Solving the Backward Problem for the Time-Fractional Diffusion Equation

This paper deals with the backward problem of a nonhomogeneous time-fractional diffusion equation, that is, the problem of determining the past distribution of the substance from present measurements. By the separation of variables method, exact solutions of the forward and backward problems are obtained in terms of eigenfunctions and Mittag-Leffler functions. Contrary to the forward problem, i.e., determining the present solution from given initial data, the backward problem, i.e., the problem of recovering the initial condition from noisy measurements of the final data, is proved to be ill-posed and highly unstable with respect to perturbations in the final data, and thus, some regularization technique is required. The novelty of the current work stems from utilizing the homotopy analysis method as a tool to obtain a regularization scheme to tackle the instability of the backward problem. Stability and convergence results of the proposed method are proved, and optimal convergence rates of the regularized solution are given under both a priori and a posteriori parameter choice rules. The resulted algorithm is very efficient and computationally inexpensive. Numerical examples are presented to illustrate the validity and accuracy of the proposed homotopy method.

 

Mohammad F. Al-Jamal


 

JJMS, 2023, 16(4), 763-788

 

 

On Hereditary, Semihereditary and Quasi-Hereditary Ternary Rings

In this paper, we define right hereditary, semihereditary and quasi- hereditary ternary rings, as previously introduced in binary rings. We show that, if a ternary ring T is completely reducible, then every right ideal I of T is of the form I = e.1.T , where e is an idempotent. Consequently, T is a right hereditary ternary ring. We also prove that, if a reduced ternary ring T satisfies the minimal condition on right annihilators of idempotents, and if I 0 is a right ideal satisfying the condition: (for every right ideal K ⊂ I, there exists a minimal right ideal H of T such that H ⊂ K), then I is projective as a right T –module. Finally, we show that if T is a semiprimary ternary ring in which the Jacobson radical = {0}, then T is a right hereditary and quasi-hereditary ternary ring.

 

Mohamed Kheir Ahmad
Safwan Aouira
Rasha Alhaj Esmaeel Arabi




 

 

JJMS, 2023, 16(4), 789-803

 

New Matrix Interpolating Inequalities

The main goal of this article is to present new generalizations and new forms of some well known matrix inequalities. These inequalities can be thought of as interpolating inequalities between the arithmetic-geometric mean inequality and Cauchy-Schwarz inequalities, generalizing some recent results in this direction.

 

M. Alakhrass
M. Sababheh



 

JJMS, 2023, 16(4), 805-815