Fixed Point Results in Controlled Metric Spaces with Applications

Abdullah Eqal Al-Mazrooei and Jamshaid Ahmad
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Abdullah Eqal Al-Mazrooei: Department of Mathematics, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia
Jamshaid Ahmad: Department of Mathematics, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia

Mathematics, 2022, vol. 10, issue 3, 1-15

Abstract: The aim of this paper is to obtain some common fixed point theorems for generalized contractions involving certain control functions in controlled metric space and derive some generalized fixed point results as a consequence of our main results. We also prove some common fixed point theorems in controlled metric spaces endowed with a graph. Our results will generalize and amend many famous results from the literature. We also provide an example to show the authenticity of the established results. As an application of our main result, we investigate the solution of integral equations.

Keywords: fixed point; controlled metric spaces; control functions; graphs; integral equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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