Journal
AIMS MATHEMATICS
Volume 7, Issue 1, Pages 315-333Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/math.2022022
Keywords
intuitionistic fuzzy set; intuitionistic fuzzy fixed point; b-metric space; Ulam-Hyers stability; integral inclusion
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Funding
- Taif University, Taif, Saudi Arabia [TURSP-2020/160]
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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. The concept of stability and well-posedness of functional inclusions involving intuitionistic fuzzy set-valued maps is introduced. Novel sufficient criteria for existence of solutions to an integral inclusion are investigated.
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 (alpha, beta)-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.
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