Two Types of Proximal Connected-Image Contractions in b-Metric Spaces and Applications to Fractional Differential Models

Mathematics 2026 Open access

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Authors: Khuanchanok Chaichana, Ben Wongsaijai, Adsadang Himakalasa, Phakdi Charoensawan
DOI: 10.3390/math14020262
Cited by: 1
References: 15

Abstract

In this paper, we introduce a new class of proximal connected-image contractions in the framework of b-metric spaces endowed with a directed graph. By employing auxiliary functions, we establish several existence and uniqueness results for best proximity points and fixed points under appropriate contractive conditions. To demonstrate the applicability of our theoretical findings, we apply the main results to a class of fractional differential equations, showing the effectiveness of the proposed approach.

Fields of Study & Subjects

Fixed Point Theorems Analysis Optimization and Variational Analysis Nonlinear Differential Equations Analysis

Publication details

Journal / source
Mathematics
Publisher
MDPI AG
Volume
14
Issue
2
Pages
262–262
Publication date
9 January 2026
Language
EN