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Since the topological properties of a b-metric space (which generalizes the concept of a metric space) seem sometimes counterintuitive due to the fact that the “open” balls may not be open sets, we review some aspects of these spaces concerning compactness, metrizability, continuity and fixed points. After doing so, we introduce new types of contractivities that extend the concept of Banach contraction. We study some of their properties, giving sufficient conditions for the existence of fixed points and common fixed points. Afterwards, we consider some iterative schemes in quasi-normed spaces for the approximation of these critical points, analyzing their convergence and stability. We apply these concepts to the resolution of a model of integral equation of Urysohn type. In the last part of the paper, we refine some results about partial contractivities in the case where the underlying set is a strong b-metric space, and we establish some relations between mutual weak contractions and quasi-contractions and the new type of contractivity.

In this paper, we present some results on the existence and uniqueness of common fixed points on d*-complete topological spaces. Our results generalize and improve upon earlier results in the literature. Finally, we give some examples in lp spaces, (p∈(0,1)), where we use the obtained results.

In this paper, we present some fixed point results for Subrahmanyan contraction in the setting of a b-metric space. We consider the case of multivalued operators. We also deduce the Ulam–Hyers stability property of the fixed point inclusion. The notion of b-metric generalizes the one of a metric, as in the third condition, the right-hand side is multiplied by a real number greater than 1. We remark that the second axiom, i.e., the one which shows the symmetry of the b-metric, remains unchanged. The findings presented in this paper extend some recent results which were proved in the context of a metric space. Some open questions are presented at the end of the paper.

In this study, we utilize the notion of triple controlled metric type space that preserves the symmetry property, which is a generalization of b-metric-type spaces, to prove new fixed-point results. We introduce (α-F)-contractive mappings and Θ-contractive mappings on triple controlled metric type space settings. Then, we establish the existence and uniqueness of fixed-point results on complete triple controlled metric type space. Moreover, some examples and applications to boundary-value problems of the fourth-order differential equation are presented to display the usage of the obtained result.

In this paper, we introduce some new types of extended Geraghty contractions, called (α,β)-admissible generalized Geraghty F-contractions, and prove some fixed point results for such contractions in the setting of partial b-metric spaces. Moreover, based on the obtained fixed point results and the property of symmetry, we inaugurate a fixed point result for graphic generalized Geraghty F-contractions defined on partial metric spaces endowed with a directed graph. As an application, we examine the existence of a unique solution to the first-order periodic boundary value by the obtained fixed point result. Moreover, some examples are presented to illustrate the validity of the new results.

In this article, we employ the notion of coupled fixed points on a complete b-metric space endowed with a graph to give sufficient conditions to guarantee a solution of system of differential equations with impulse effects. We derive recisely some new coupled fixed point theorems under some conditions and then apply our results to achieve our goal.

In this paper, we introduce the notion of cyclic ( α , β ) ⁻ ( ψ , φ ) s -rational-type contraction in b-metric spaces, and using this contraction, we prove common fixed point theorems. Our work generalizes many existing results in the literature. In order to highlight the usefulness of our results, applications to functional equations are given.