Fixed Point Theorems of Almost Generalized Contractive Mappings in b -Metric Spaces and an Application to Integral Equation

N. Seshagiri Rao, Zoran D. Mitrović (), Dania Santina and Nabil Mlaiki
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N. Seshagiri Rao: Department of Mathematics & Statistics, School of Applied Science & Humanities, Vignan’s Foundation for Science, Technology & Research, Vadlamudi, Guntur 522213, India
Zoran D. Mitrović: Faculty of Electrical Engineering, University of Banja Luka, Patre 5, 78000 Banja Luka, Bosnia and Herzegovina
Dania Santina: Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
Nabil Mlaiki: Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia

Mathematics, 2023, vol. 11, issue 11, 1-19

Abstract: In this study, we have new fixed point results for weak contraction mappings in complete and partially ordered b -metric spaces. Our findings expand and generalize the results of Jachymski and Mituku et al and many more results in the literature as well. To illustrate our work, we present an application on the existence and uniqueness of a nonlinear quadratic integral problem solution. Moreover, an open problem is presented to enable the scope for future research in this area.

Keywords: b -metric space; weak contractions; fixed point, compatible and weakly compatible mappings; coupled coincidence point; nonlinear quadratic integral equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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