Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics
- P-ISSN : 3059-0604
- E-ISSN : 3059-1309
- Publisher : Korean Society of Mathematical Education
- P-ISSN3059-0604
- E-ISSN3059-1309
- KCI
Latest Articles
Vol.33 No.1
6papers in this issue.
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Employing Fixed Point Theorems to Establish Existence Results for a System of Coupled Hybrid Fractional Differential Equations with Three Variables
Shirish P Kulkarni ; Soni Pathak ; Tauhid Ali Khalique Ali Sayyed ; Prerana Rahul Lale
pp.1-19
https://doi.org/10.7468/jksmeb.2026.33.1.1
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Abstract
This study explores the existence of solutions for a system of coupled hybrid fractional differential equations (HFDEs) involving three variables. By applying appropriate boundary conditions, we establish sufficient criteria for solution existence using fundamental fixed-point theorems, such as Banach’s and Schauder’s theorems. The analysis is made more difficult by the equations’ hybrid structure, which combines continuous and discrete variables with fractional derivatives. The problem formulation is presented, appropriate spaces for the unknown functions are defined, and criteria for applying fixed-point theorems are derived. Our findings provide a more thorough framework for simulating intricate dynamic systems by adding multi-variable interactions and hybrid components to the current literature on fractional differential equations.
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Fixed Point Theorems Satisfying Geraghty-type Contraction on relational Multiplicative Metric Spaces with Application
Amrish Handa ; Sonal Jain
pp.21-36
https://doi.org/10.7468/jksmeb.2026.33.1.21
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Abstract
The principal objective of this research article is to construct a unique common fixed point theorem satisfying Geraghty-type contraction on relational multiplicative metric spaces. We study the existence and uniqueness of a solution for multiplicative boundary value problems and an example is also given to validate our results. Our results improve and generalize various classical and recent results in the existing literature of multiplicative metric spaces.
Muhammad Bilal ; Muhammad Imtiaz ; Asif R. Khan ; Ihsan Ullah ; Muhammad Zafran
pp.37-61
https://doi.org/10.7468/jksmeb.2026.33.1.37
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Abstract
In this paper, we establish the Hermite-Hadamard dual inequality for the class of (s, r)-convex functions. Furthermore, we present several additional results related to the Hermite-Hadamard inequality for (s, r)-convex functions by employing Riemann-Liouville fractional integrals through distinct techniques. As a consequence, various known results are obtained as special cases. In addition, we provide applications of our findings in terms of special means.
Muhammad Shabbir ; Asif R. Khan ; Muhammad Bilal
pp.63-76
https://doi.org/10.7468/jksmeb.2026.33.1.63
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Abstract
In this study, we present two distinct functions associated with the left and right bounds of the fractional Hermite-Hadamard inequality. Furthermore, we establish and prove several results concerning these bounds within the framework of Lipschitz continuous functions.
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Several New Formulas for a Class of Improper Integrals Whose Integrands Contain the Powers of the Sine Function
Feng Qi
pp.77-88
https://doi.org/10.7468/jksmeb.2026.33.1.77
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Abstract
In the paper, the author briefly reviews and unifies some known formulas and satisfactorily presents several new formulas for a class of improper integrals whose integrands contain the powers of the sine function.
Gopi Prasad ; Sheetal Deshwal ; Souvik Kundu
pp.89-98
https://doi.org/10.7468/jksmeb.2026.33.1.89
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Abstract
The present study aims to investigate the bivariate case as well as the GBS generalization of modification of Gamma operators studied by Usta and Betus [24]. This article considers the definition of the bivariate case of modified Gamma operators discussed by Usta and Betus. After which GBS defined and their approximation properties are discussed on B¨ogel spaces. In addition to that, some graphical examples are presented to verify our theoretical results using Matlab. Using a graphical representation, we conclude by comparing the bivariate example and the GBS generalization of these operators.