Relaxing the Φ-Family Auxiliary Functions and Related Results

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...

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Bibliographic Details
Main Authors: Salvatore Sessa, Yahya Almalki, Monairah Alansari, Muhammad Usman Ali, Essam Saleh Saad Said Al-Yari
Format: Article
Language:English
Published: MDPI AG 2025-04-01
Series:Axioms
Subjects:
Online Access:https://www.mdpi.com/2075-1680/14/4/268
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Summary: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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Δ</mo></semantics></math></inline-formula>-family, which simplifies the axioms in comparison to the previously defined <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Φ</mo></semantics></math></inline-formula>-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.
ISSN:2075-1680