No abstract

No abstract

In this article, utilizing the concept of w-distance, we prove the celebrated Banach's fixed point theorem in metric spaces equipped with an arbitrary binary relation. Necessarily our findings unveil another direction of relation-theoretic metrical fixed point theory. Also, our paper consists of several non-trivial examples which signify the motivation for such investigations. Finally, our obtained results enable us to explore the existence and uniqueness of solutions of nonlinear fractional differential equations involving the Caputo fractional derivative.2010 Mathematics Subject Classification. 47H10, 54H25.

In this paper, we study an interesting generalization of standard metric spaces, b-metric spaces, dislocated metric spaces, and modular spaces due to the recent work of Jleli and Samet. Here we modify the result forĆirić quasi-contraction-type mappings and also prove the same result by taking D-admissible mappings. Moreover, we establish fixed point theorems for two well-known nonlinear contractions like rational contraction mappings and Wardowski type contraction mappings. Several important results in the literature can be derived from our results. Suitable examples are presented to substantiate our obtained results.

In this paper, we introduce the notions of generalized α-F -contraction and modified generalized α-F -contraction. Then, we present sufficient conditions for existence and uniqueness of fixed points for the above kind of contractions. Necessarily, our results generalize and unify several results of the existing literature. Some examples are presented to substantiate the usability of our obtained results. MSC: 47H10; 54H25.So, (X, d) is a complete metric space. Now d(gx, gy) > 0 for (x, y) = (0, 1) and (x, y) = (−1, 1). Therefore we consider the following two cases.