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In this paper, we introduce the notion of generalized (α,ϕ)-Meir–Keeler hybrid contractive mappings of type I and II via simulation function and establish fixed point theorems for such mappings in the setting of complete b-metric spaces. Our results extend and generalize many related fixed point results in the existing literature. Finally, we provide an example in support of our main finding.

In this paper, we introduce the class of rectangular quasi b-metric spaces as a generalization of rectangular metric spaces, rectangular quasi-metric spaces, rectangular b-metric spaces, define generalized (α,ψ)-contraction mappings and study fixed point results for the maps introduced in the setting of rectangular quasi b-metric spaces. Our results extend and generalize related fixed point results in the literature, in particular, the works of Karapinar and Lakzian (J. Funct. Spaces 2014:914398, 2014), Alharbi et al. (J. Math. Anal. 9(3):47–60, 2018), and Khuangsatung et al. (Thai J. Math. 2020:89–101, 2020) from rectangular quasi metric space and rectangular b-metric space to rectangular quasi b-metric spaces. We also provide examples in support of our main findings. Furthermore, we applied one of our results to determine the existence of a solution to an integral equation.

This paper aims to demonstrate some common fixed point results for a pair of self-mappings satisfying ( L b − ϑ − ψ ) -contractivity condition through b -simulation function in the setup of b -metric spaces. The presented results generalize, complement, and improve some corresponding results in this direction. Furthermore, we draw some corollaries from our results and provide an example to show the applicability and validity of our findings. As an application of our result, we discuss the existence of a solution to a nonlinear integral equation.

In this study, we manifest a new class of mappings that satisfy Geraghty–Ćirić-type contractive conditions in the context of b-metric spaces and prove a theorem on the existence and uniqueness of fixed points. Our results unify and generalize the results of Geraghty; Ćirić; Dukic, Kadelburg, and Radenović; and Shu-fang Li, Fei Hi, and Ning Lu in the setting of b-metric spaces. Furthermore, we provide examples to verify the correctness and applicability of our results. We also utilize our findings to show the existence of a unique solution for a nonlinear integral equation.

In this paper, we introduce generalized α,ψ-contraction mappings in the setting of rectangular b-metric spaces and established existence and uniqueness of fixed points for the mappings introduced. Our results extend and generalize related fixed point results in the existing literature. We derive some consequences and corollaries from our obtained results. Also, we provide examples in support of our main findings. Furthermore, we determined a solution to an integral equation by applying our obtained results.

In this paper, we introduce an almost generalized α-admissible Z-contraction with the help of a simulation function and study fixed point results in the setting of partially ordered b-metric spaces. The presented results generalize and unify several related fixed point results in the existing literature. Finally, we verify our results by using two examples. Moreover, one of our fixed point results is applied to guarantee the existence of a solution of an integral equation.

In this paper, we establish fixed point theorems for α-F-convex contraction mappings in b-metric space and prove the existence and uniqueness of fixed points for such mappings. Our result extends and generalizes comparable results in the existing literature. Finally, we provide an example in support of our main finding.

Abstract Objectives In this paper we introduce fixed point theorems for generalized rational type $$\\alpha$$ α -admissible contractive mappings in partially ordered b-metric spaces and prove the existence and uniqueness of fixed points for self-mappings satisfying the established theorems. Finally, we provide examples in support of our main findings in the setting of partially ordered b-metric spaces. Result New fixed point results have been obtained for generalized rational type $$\\alpha$$ α -admissible contractive mappings in the setting of partially ordered b-metric space and we applied one of our results to determine a solution to an integral equation.

This paper focuses on existence and uniqueness of common fixed points for a pair of self-mapping satisfying generalized rational type ϑ,ψ,φ-weak contractive condition in which one of the mapping is α-admissible with respect to the other and weakly compatible mappings in the framework of b-metric spaces. The results presented herein generalize and improve some well-known results in the existing literature. Furthermore, we draw some corollaries from our results and provide an example for illustrating the validity of our findings. As an application of our result, we discuss the existence of a solution to a fractional order differential equation.

This paper focuses on existence and uniqueness of common fixed points for a pair of self‐mapping satisfying generalized rational type ( ϑ , ψ , φ )‐weak contractive condition in which one of the mapping is α ‐admissible with respect to the other and weakly compatible mappings in the framework of b ‐metric spaces. The results presented herein generalize and improve some well‐known results in the existing literature. Furthermore, we draw some corollaries from our results and provide an example for illustrating the validity of our findings. As an application of our result, we discuss the existence of a solution to a fractional order differential equation.