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In this paper, the concept of convex rectangular b − metric spaces is introduced as a generalization of both convex metric spaces and rectangular b − metric spaces. The purpose of this study is to indicate a way of generalizing Mann's iteration algorithm and a series of fixed point results in rectangular b − metric spaces. Furthermore, certain examples are given to support the results. We also study well posedness of fixed point problems of some mappings in convex rectangular b − metric spaces, and an application to the dynamic programming is entrusted to manifest the viability of the obtained results. Our results extend comparable results in the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence and uniqueness of fixed points for F -contractions in complete Branciari b -metric spaces. Furthermore, an example for supporting the related result is shown. We also present the concept of the weak well-posedness of the fixed-point problem of the mapping T and discuss the weak well-posedness of the fixed-point problem of an F -contraction in complete Branciari b -metric spaces. Besides, we investigate the problem of common fixed points for F -contractions in above spaces. As an application, we apply our main results to solving the existence and uniqueness of solutions for a class of the integral equation and the dynamic programming problem, respectively. [ABSTRACT FROM AUTHOR]