Work

Dual Connected-Image Contractions for a Pair of Mappings in Directed Graph Metric Spaces with Applications

Year: 2026

Type: article

Abstract: In this paper, we introduce a new class of contractions, called dual connected-image contractions, for a pair of self-mappings on a metric space endowed with a directed graph. This concept extends the notion of connected-image contractions by incorporating the interaction between two mappings through the graph structure. By employing a class of auxiliary functions, we establish existence and uniqueness results for common fixed points under this generalized contractive framework. The proposed approach not only unifies and extends several known results in the literature but also provides greater flexibility in handling nonlinear problems. As an application, the theoretical results are applied to a class of nonlinear fractional differential equations with nonlocal integral boundary conditions, where the existence of solutions is established by reformulating the problems as equivalent integral equations and applying the developed common fixed point framework.

Source: Mathematics

DOI: 10.3390/math14122173

Authors: Khuanchanok Chaichana, Wanchalerm Sucpikarnon, Phakdi Charoensawan

Institutions: Centre of Excellence in Mathematics, Ministry of Higher Education, Science, Research and Innovation, Chiang Mai University

Language: English

Topic: Fixed Point Theorems Analysis

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funders: Chiang Mai University, Thailand Science Research and Innovation, Centre of Excellence in Mathematics, Mahidol University