Search

One of the tools for building new fixed-point results is the use of symmetry in the distance functions. The symmetric property of metrics is particularly useful in constructing contractive inequalities for analyzing different models of practical consequences. A lot of important invariant point results of crisp mappings have been improved by using the symmetry of metrics. However, more than a handful of fixed-point theorems in symmetric spaces are yet to be investigated in fuzzy versions. In accordance with the aforementioned orientation, the idea of Presic-type intuitionistic fuzzy stationary point results is introduced in this study within a space endowed with a symmetrical structure. The stability of intuitionistic fuzzy fixed-point problems and the associated new concepts are proposed herein to complement their corresponding concepts related to multi-valued and single-valued mappings. In the instance where the intuitionistic fuzzy-set-valued map is reduced to its crisp counterparts, our results complement and generalize a few well-known fixed-point theorems with symmetric structure, including the main results of Banach, Ciric, Presic, Rhoades, and some others in the comparable literature. A significant number of consequences of our results in the set-up of fuzzy-set- and crisp-set-valued as well as point-to-point-valued mappings are emphasized and discussed. One of our findings is utilized to assess situations from the perspective of an application for the existence of solutions to non-convex fractional differential inclusions involving Caputo fractional derivatives with nonlocal boundary conditions. Some nontrivial examples are constructed to support the assertions and usability of our main ideas. [ABSTRACT FROM AUTHOR]

In this paper, new intuitionistic fuzzy fixed point results for sequence of intuitionistic fuzzy set-valued maps in the structure of b-metric spaces are examined. A few nontrivial comparative examples are constructed to keep up the hypotheses and generality of our obtained results. Following the fact that most existing concepts of Ulam-Hyers type stabilities are concerned with crisp mappings, we introduce the notion of stability and well-posedness of functional inclusions involving intuitionistic fuzzy set-valued maps. It is a familiar fact that solution of every functional inclusion is a subset of an appropriate space. In this direction, intuitionistic fuzzy fixed point problem involving (α,β)-level set of an intuitionistic fuzzy set-valued map is initiated. Moreover, novel sufficient criteria for existence of solutions to an integral inclusion are investigated to indicate a possible application of the ideas presented herein.

In this paper, we prove a fixed point theorem for intuitionistic fuzzy mappings concerning F-contractions without using the Pompeiu – Hausdorff distance between cut sets of intuitionistic fuzzy mappings. This result and its consequences extend and generalize several results in the literature. An application to the existence for solutions of a delay integral equation of Volterra type and an example are given to illustrate the usability of our results. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to prove some new common fixed point and coincidence point theorems for a pair of intuitionistic fuzzy mappings on a complete metric linear space in association with the Hausdorff metric as well as d1 metric on the family of intuitionistic fuzzy sets (IFS). Moreover, as an application, in function space C [a; b], an existence of coincidence theorem for a family of nonlinear integral equations has been established. Some illustrative examples which demonstrate the validity of the hypothesis and novelty of our main results are presented. [ABSTRACT FROM AUTHOR]