In this paper, we have established some fixed point theorems in the context of strong b-metric spaces. For this purpose, Ciric type contraction for single-valued mapping and Nadler’s type Banach and Chatterjea contractions for set-valued mappings are applied to obtain fixed point and common fixed points. A simple and different technique has been used to obtain the results. Our results unify, extend and generalize the existence of corresponding present and conventional results existing in the literature of fixed point theory.

On Coincidence Theorem in Intuitionistic Fuzzy b-Metric Spaces with Application: The concept of intuitionistic fuzzy b-metric spaces (shortly, IFbMS) has been introduced and studied to generalize both the notion of intuitionistic fuzzy metric spaces and fuzzy b-metric spaces. The existence of coincident point and common fixed point for two self-mappings has been established. In order to show the strength of these results, some interesting examples are established as well. Our results generalize many previous results existing in literature. Some nontrivial examples are furnished as well as an application is created to give the strength of our main result.

In the present research, modern fuzzy technique is used to generalize some conventional and latest results. The objective of this paper is to construct and prove some fixed-point results in complete fuzzy strong b-metric space. Fuzzy strong b-metric (sb-metric) spaces have very useful properties such as openness of open balls whereas it is not held in general for b-metric and fuzzy b-metric spaces. Due to its properties, we have worked in these spaces. In this way, we have generalized some well-known fixed-point theorems in fuzzy version. In addition, some interesting examples are constructed to illustrate our results.

In this research article, fixed point theory is beautifully combined with fuzzy set theory. Two fuzzy fixed point theorems of L-fuzzy mappings are established and proved for two different contractive type conditions in the scenario of complete b-metric space. In order to give the strength of these results, nontrivial supportive examples for both results are also provided. The notion of L-fuzzy mappings is a generalized form of fuzzy mappings as well as multivalued mappings. In this approach, our results provide uniqueness, extension, and successive generalizations of many valuable recent and conventional results existing in the literature.

The main focus of the present paper is to establish a common coincidence point theorem for a pair of L -fuzzy mappings and a non-fuzzy mapping under a generalized φ -contractive condition on a metric space in association with the Hausdorff distance on a class of L -fuzzy sets. A generalized common coincidence point theorem with the d L ∞ metric on 1- cuts of L -fuzzy sets is also obtained, which generalizes many recent results in literature. As applications, an analogous coincidence point theorem for crisp mappings is achieved to study some existence theorems of solution for a class of nonlinear integral equations. Even as direct application of coincidence of L - fuzzy mappings, an implicit function theorem is established which can be used to find an explicit restriction of a given implicit relation. For verification and elaboration of our results some interesting and non-trivial examples are presented as well.