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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 contains results of the existence of fuzzy fixed points of fuzzy mappings that satisfy certain contraction conditions using the platform of partial b-metric spaces. Some non-trivial examples are provided to authenticate the main results. The constructed results in this work will likely stimulate new research directions in fuzzy fixed-point theory and related hybrid models. Eventually, some fixed-point results on multivalued mappings are established. These theorems provide an excellent application of main theorems on fuzzy mappings. The results of this article are extensions of many already existing results in the literature.

Recently, Ji et al. established certain fixed-point results using Mann’s iterative scheme tailored to Gb-metric spaces. Stimulated by the notion of the F-contraction introduced by Wardoski, the contraction condition of Ji et al. was generalized in this research. Several fixed-point results with Mann’s iterative scheme endowed with F-contractions in Gb-metric spaces were proven. One non-trivial example was elaborated to support the main theorem. Moreover, for application purposes, the existence of the solution to an integral equation is provided by using the axioms of the proven result. The obtained results are generalizations of several existing results in the literature. Furthermore, the results of Ji. et al. are the special case of theorems provided in the present research.

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 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.

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.