Work

Relaxed contractions in suprametric spaces: A unified framework with applications to nonlinear differential models

Year: 2026

Type: article

Abstract: This paper develops a relaxed fixed-point framework for nonlinear operators acting on suprametric spaces. A new class of control functions $ \Theta^{R} $ is introduced, allowing strictly increasing but possibly discontinuous behaviors that go beyond the classical $ \vartheta $-contraction structure. Within this setting, several relaxed $ \vartheta _{\mathcal{R}} $-type contractive conditions are formulated through max-based suprametric functionals and on complete suprametric spaces. These conditions guarantee the existence and uniqueness of fixed-points under a suitable jump requirement on the control function. The theory is supported by explicit examples showing how discontinuities and nonlinear growth patterns influence convergence. Finally, two differential models, namely a second-order particle motion problem and a fourth-order beam equation, are used to demonstrate that their associated integral operators admit unique solutions within the proposed relaxed suprametric framework.

Source: AIMS Mathematics

DOI: 10.3934/math.2026372

Authors: Abdurrahman Büyükkaya, Ekber Girgin, Haroon Ahmad, Mudasir Younis, Mahpeyker Öztürk

Institutions: Sakarya Uygulamalı Bilimler Üniversitesi, Government College University, Lahore, Sakarya University, Saveetha University

Language: English

Topic: Fixed Point Theorems Analysis

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,200

OpenAlex ID: W7148846627