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This paper presents two fixed point results for both single valued and multivalued mappings on F-metric spaces, which is introduced by Jleli and Samet [1]. First, we consider the concept of P-contraction for single valued mappings. Then using the Feng-Liu’s technique, we present a fixed point result for F-closed set valued mappings on F-metric spaces.

In this paper, we elucidate a pivotal fixed point theorem for P-contraction mappings defined on M-metric spaces, offering a novel perspective on the interplay between mappings and the underlying space structure. This theorem's significance becomes evident when compared with earlier results, underscoring its potential to enhance our understanding of fixed point theory in M-metric spaces and its broader applications. [ABSTRACT FROM AUTHOR]

In this paper, we aim to overcome the problem given by Abkar et al. [Abstr. Appl. Anal., 2013 (2013), 189567], and so to obtain real generalizations of fixed point results in the literature. In this direction, we introduce a new class of functions, which include R-functions. Thus, we present a new type of R-contraction and weaken R-contractions that have often been studied recently. We also give a new definition of the P-property. Hence, we obtain some best proximity point results, including fixed point results for the new kind of R-contractions. Then, we provide an example to show the effectiveness of our results. Finally, inspired by a nice and interesting technique, we investigate the existence of a best proximity point of the homotopic mappings with the help of our main result. [ABSTRACT FROM AUTHOR]

By implying α-admissible mapping, this study expands and investigates generalized contraction mappings in quasi-metric spaces, aiming to establish the existence of fixed points. Moreover, we show that the main outcomes of the paper encompass several previously reported results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we present some fixed point results for multivalued mappings with both closed values and proximinal values on left K-complete quasi metric spaces. We also provide a nontrivial example to illustrate our results.

In this work, taking into account the theta-function, we present a general class of multivalued weakly Picard operators on complete metric space. We also provide an example showing that it includes some earlier classes as properly.

We introduce the new idea of (α − θ σ) -contraction in quasi-metric spaces in this paper. For these kinds of mappings, we then prove new fixed-point theorems on left K, left M, and left S m y t h -complete quasi-metric spaces. We also apply our results to infer the existence of a solution to a second-order boundary-value problem. [ABSTRACT FROM AUTHOR]

This article studies new classes of contractions called the p-cyclic Reich contraction and p-cyclic Reich contraction pair and develops certain best proximity point results for such contractions in the setting of partial metric spaces. Furthermore, the best proximity point results for p-proximal cyclic Reich contractions of the first and second types are also discussed. [ABSTRACT FROM AUTHOR]

In the present paper, we define the Pw-contraction by considering the inequality called P-contraction in metric space together with the w-distance. We then present fixed point theorems for both singlevalued and multivalued Pw-contractions. We also support our results with suitable examples. [ABSTRACT FROM AUTHOR]

The purpose of this article is to present the notion of graphical extended b-metric spaces, blending the concepts of graph theory and metric fixed point theory. We discuss the structure of an open ball of the new proposed space and elaborate on the newly introduced ideas in a novel way by portraying suitably directed graphs. We also provide some examples in graph structure to show that our results are sharp as compared to the results in the existing state-of-art. Furthermore, an application to the transverse oscillations of a homogeneous bar is entrusted to affirm the applicability of the established results. Additionally, we evoke some open problems for enthusiastic readers for the future aspects of the study. [ABSTRACT FROM AUTHOR]