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This paper introduces the concept of ( P , ψ ) -type almost contractive conditions for fuzzy mappings in b -metric spaces. This novel framework is employed to establish certain fuzzy fixed point results in complete b -metric spaces. An illustrative example is provided to validate the assumptions of the main theorem, ensuring the existence of fuzzy fixed points. Furthermore, the existence of a solution to a second-order nonlinear boundary value problem is demonstrated by transforming the problem into a fixed point equation and applying the proven results. Several corollaries are derived as consequences of the main findings. The results presented in this work extend and generalize numerous existing fixed point theorems in the literature.

In this article, we obtain some fixed-point results involving α-admissibility for multivalued F-contractions in the framework of partial b-metric spaces. Appropriate illustrations are provided to support the main results. Finally, an application is developed by demonstrating the existence of a solution to an integral equation.

This article introduces the concept of generalized (ffF,b,ϕ˘) contraction in the context of b-metric spaces by utilizing the idea of F contraction introduced by Dariusz Wardowski. The main findings of the research focus on the existence of best proximity points for multi-valued (ffF,b,ϕ˘) contractions in partially ordered b-metric spaces. The article provides examples to illustrate the main results and demonstrates the existence of solutions to a second-order differential equation and a fractional differential equation using the established theorems. Additionally, several corollaries are presented to show that the results generalize many existing fixed-point and best proximity point theorems.

Motivated by the ideas of F-weak contractions and F,Rg-contractions, the notion of Fw,Rg-contractions is introduced and studied in the present paper. The idea is to establish some interesting results for the existence and uniqueness of a coincidence point for these contractions. Further, using an additional condition of weakly compatible mappings, a common fixed-point theorem and a fixed-point result are proved for Fw,Rg-contractions in metric spaces equipped with a transitive binary relation. The results are elaborated by illustrative examples. Some consequences of these results are also deduced in ordered metric spaces and metric spaces endowed with graph. Finally, as an application, the existence of the solution of certain Voltera type integral equations is investigated.

In this manuscript, we establish some fixed point results for fuzzy mappings via α∗,F -contractions. For validation of the proved results, some nontrivial examples are presented. Few interesting consequences are also stated which authenticate that our results generalize many existing ones in the literature.

This study pioneers the introduction of two novel concepts in the realm of double‐controlled metric spaces: the Θ ‐fuzzy double‐controlled contraction mapping and the Θ ‐fuzzy almost generalized double‐controlled contraction mapping. These concepts represent a significant expansion of the existing framework of generalized contractions. This research establishes the existence and uniqueness of fixed points for each of these contraction mappings and provides exemplary illustrations to clarify the results. Moreover, we demonstrate the practical applicability of our findings by showing the existence of a solution to a nonlinear differential equation. The established theorems also yield various corollaries, which confirm that our results generalize and extend previously established findings in the field.

In this study, we present a more general class of rational-type contractions in the domain of Hilbert spaces, along with a novel coupled implicit relation. We develop several intriguing results and consequences for the existence of unique coupled fixed points. Further, we investigate a necessary condition that guarantees the well-posedness of a coupled fixed-point problem of self-mappings in Hilbert spaces. Some new observations proposed in this research broaden and extend previously published results in the literature.

This article is focused on the generalization of some fixed point theorems with Kannan-type contractions in the setting of new extended b-metric spaces. An idea of asymptotic regularity has been incorporated to achieve the new results. As an application, the existence of a solution of the Fredholm-type integral equation is presented.

This article is based on the concept of partial extended b-metric spaces, which is inspired by the notions of new extended b-metric spaces and partial metric spaces. Fixed point results for single and multivalued mappings on such spaces are also presented. Few examples are also provided to elaborate the concepts.

In this paper we generalize the notion of ...-valued contraction mappings, recently introduced by Ma et al., by weakening the contractive condition introduced by them. Using the new notion of ...-Valued contractive type mappings, we establish a fixed point theorem for such mappings. Our result generalizes the result by Ma et al. and those contained therein except for the uniqueness.