Work

Relaxing the Φ-Family Auxiliary Functions and Related Results

Year: 2025

Type: article

Abstract: This article establishes the existence of fixed points and common fixed points for set-valued mappings satisfying an implicit-type contraction inequality involving a new auxiliary function in a complete metric space equipped with a binary relation. Through a novel family of functions referred to as the Δ-family, which simplifies the axioms in comparison to the previously defined Φ-family, the study unifies a few classical fixed-point theorems. The practical relevance of the theoretical findings is demonstrated by applying the results to investigate the existence of solutions for a system of integral equations.

Source: Axioms

DOI: 10.3390/axioms14040268

Authors: Salvatore Sessa, Yahya Almalki, Monairah Alansari, Muhammad Usman Ali, Essam Saleh Saad Said Al-Yari

Institutions: University of Naples Federico II, King Khalid University, King Abdulaziz University, COMSATS University Islamabad

Language: English

Topic: Fixed Point Theorems Analysis

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: King Khalid University