Work

Study of Existence and Stability of Fixed Points of Hypotenuse Contracting Mappings with Applications to Parabolic PDE

Year: 2026

Type: preprint

Abstract: In this article, we introduce a novel class of mappings identified by their property of contracting the hypotenuse of a right-angled triangle in the setting of metric spaces. We establish sufficient conditions ensuring both the existence and uniqueness of fixed points. A geometric analysis, complemented by illustrative diagrams, is provided to differentiate these mappings from other familiar contraction types, namely perimeter and area contractions, supported by examples. Furthermore, we investigate the Ulam-Hyers stability of the associated fixed point equation, thereby strengthening the robustness of the theoretical framework. Finally, the derived results are applied to demonstrate the existence of solutions for a nonhomogeneous linear parabolic partial differential equation (PDE).

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.17761

Authors: Roy, Kushal, Banerjee, Anish, Dey, Lakshmi Kanta

Institutions: Dr. B.C. Roy Engineering College, National Institute of Technology Durgapur

Language: English

Topic: Fixed Point Theorems Analysis

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7203752522

Cites: 1

Cited by:

Related to: 10