Existence of ${\alpha }_L$-Fuzzy Fixed Points of L-Fuzzy Mappings

Abstract

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.

A Comprehensive Study on Advancement in Hybrid Contraction and Graphical Analysis of £-Fuzzy Fixed Points with Application

“…For more results in this regard, see [31,32]. The present article inaugurates the modified form of an admissible hybrid fuzzy Z-contraction in the bodywork of £-FS-valued maps for extended -MSs and furnished the sufficient criteria for £-FFP results.…”

Fixed Point and Common Fixed Point Theorems for Single Valued and Multivalued Mappings in Partial b-Metric Spaces

“…The aforementioned spaces have seen a great deal of development. The aforementioned spaces have recently been the focus of investigation into fixed point and common fixed point results for single-valued as well as multi-valued mappings; for examples, see Ali et al (6) , Khan et al (7) , Kanwel et al (8)(9)(10) , Tassaddiq et al (11) , Karapinar et al (12,13) , Qawaqneh et al (14) , Shoaib et al (15) , and the references within it.…”

A Fixed Point Approach to Lattice Fuzzy Set via F-Contraction

“…For α L -cut sets of L-FM, Rashid et al [5] studied FP theorems for L-FMs to the discovery of the Hausdorff distance. Common FP results on L-FPs can be seen in [5][6][7] and references therein. Heilpern [8] introduced the theory of FM and established a theorem on FP for FM in metric linear space, which serves as a fuzzy generalization of Banach's contraction principle [9].…”

“…Many works appear to ensure the existence of FPs and common FPs of FMs and L-FMs that meet a condition (see [5][6][7][8]19,20] and references therein). Moreover, in 2012, Wardowski [21] obtained a new fixed point theorem concerning F-contraction for singlevalued mapping.…”