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The main purpose of this study is to examine the existence of fuzzy fixed points of fuzzy mappings meeting the criteria of some generalized contractions of Nadler's type in the framework of complete b-metric spaces. From the pertinent literature, there are additional previous observations that are provided as corollaries. Our study expands and incorporates several implications that are apparent in this mode and are addressed in considerable literature.

A contemporary fuzzy technique is employed in the current study to generalize some established and recent findings. For researchers, fixed point (FP) procedures are highly advantageous and appealing mechanisms. Discovering fuzzy fixed points of fuzzy mappings (FM) meeting Nadler's type contraction in complete fuzzy metric space (FMS) and?iri? type contraction in complete metric spaces (MS) is the core objective of this research. The outcomes are backed up by example and applications that highlight these findings. There are also preceding conclusions that are given as corollaries from the relevant literature. In this mode, numerous consequences exist in the significant literature are extended and combined by our findings.

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.

In this note, by using basic properties of the recently introduced concepts of generalized metric spaces, new conditions for the existence of a fixed point for weakly type contractive operator which sends a closed subset into the ambient space under consideration are examined. Our obtained result extends and unifies its corresponding ideas in metric and modular spaces. A comparative non-trivial example is provided to show the novelty and preeminence of our proposed notion.

Over time, hybrid fixed point results have been examined merely in the framework of classical mathematics. This one way research has clearly dropped-off a great amount of important results, considering the fact that a fuzzy set is a natural enhancement of a crisp set. In order to entrench hybrid fixed notions in fuzzy mathematics, this paper focuses on introducing a new idea under the name intuitionistic fuzzy p -hybrid contractions in the realm of -metric spaces. Sufficient conditions for the existence of common intuitionistic fuzzy fixed points for such maps are established. In the instance where our presented results are slimmed down to their equivalent nonfuzzy counterparts, the concept investigated herein unifies and generalizes a significant number of well-known fixed point theorems in the setting of both single-valued and multivalued mappings in the corresponding literature. A handful of these special cases are highlighted and analysed as corollaries. A nontrivial example is put together to indicate that the hypotheses of our results are valid.

In this work, we design and demonstrate the occurrence of L-fuzzy common fixed points of L-fuzzy mappings (L-FM) meeting contractive criteria in the framework of complete b-metric spaces (b-MS) employing F-contractions and a certain class of continuous functions. We also conduct a case study to determine the implementation of our derived principles. A few other concepts which are the direct consequences of our findings are explained in this paper.

In this paper, the notion of $$(\varphi , F)$$ -weak contractions in the framework of metric-like spaces is introduced and the corresponding fixed point theorems are established. As an attempt to answer the common question regarding the uniqueness of trivial solutions of homogeneous integral equations on time scales, one of our main results is applied to investigate sufficient criteria for existence and uniqueness of solution of nonlinear Fredholm integral equations of the second kind on time scales. The latter result is obtained through a new Lipschitz condition on the kernel different from the usual ones. Examples are constructed to show that our ideas herein are new and generalize some recently announced results in the literature.