Fixed Point Results for Hybrid Rational Contractions under a New Compatible Condition with an Application

Xiaolan Liu; Mi Zhou; Arslan Hojat Ansari; Naeem Saleem; Mukesh Kumar Jain

doi:10.3390/math12010121

Fixed Point Results for Hybrid Rational Contractions under a New Compatible Condition with an Application

Xiaolan Liu, Mi Zhou^*, Arslan Hojat Ansari, Naeem Saleem, Mukesh Kumar Jain

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

In this scholarly discourse, we present proof of the existence of unique fixed points in b-metric spaces for hybrid rational contractions. Moreover, we establish a common fixed point theorem for four self-mappings, assuming S-compatibility for two pairs of self-mappings within the framework of b-metric spaces. As a practical demonstration of the aforementioned results, we apply them to a type of integral equation and derive a theorem that guarantees the existence of solutions.

Original language	English
Article number	121
Journal	Mathematics
Volume	12
Issue number	1
DOIs	https://doi.org/10.3390/math12010121
Publication status	Published - Jan 2024
Externally published	Yes

Keywords

C-class function
S-compatibility
b-metric space
fixed/common fixed point
rational contraction

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10.3390/math12010121

Cite this

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title = "Fixed Point Results for Hybrid Rational Contractions under a New Compatible Condition with an Application",

abstract = "In this scholarly discourse, we present proof of the existence of unique fixed points in b-metric spaces for hybrid rational contractions. Moreover, we establish a common fixed point theorem for four self-mappings, assuming S-compatibility for two pairs of self-mappings within the framework of b-metric spaces. As a practical demonstration of the aforementioned results, we apply them to a type of integral equation and derive a theorem that guarantees the existence of solutions.",

keywords = "C-class function, S-compatibility, b-metric space, fixed/common fixed point, rational contraction",

author = "Xiaolan Liu and Mi Zhou and {Hojat Ansari}, Arslan and Naeem Saleem and Jain, {Mukesh Kumar}",

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AU - Jain, Mukesh Kumar

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AB - In this scholarly discourse, we present proof of the existence of unique fixed points in b-metric spaces for hybrid rational contractions. Moreover, we establish a common fixed point theorem for four self-mappings, assuming S-compatibility for two pairs of self-mappings within the framework of b-metric spaces. As a practical demonstration of the aforementioned results, we apply them to a type of integral equation and derive a theorem that guarantees the existence of solutions.

KW - C-class function

KW - S-compatibility

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KW - fixed/common fixed point

KW - rational contraction

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ER -

Fixed Point Results for Hybrid Rational Contractions under a New Compatible Condition with an Application

Abstract

Keywords

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