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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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-04-01
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| 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. |
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| ISSN: | 2075-1680 |