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Fuzzy fixed point theorems and Ulam-Hyers stability of fuzzy set-valued maps

  • Monairah Alansari , Mohammed Shehu Shagari EMAIL logo and Akbar Azam
Published/Copyright: March 28, 2022
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Abstract

In this paper, new common fuzzy fixed point theorems for sequence of fuzzy set-valued maps in the framework of complete b-metric spaces are established. Consequently, corresponding fixed point theorems in the setting of point-to-set-valued and single-valued mappings are deduced. A few nontrivial examples which dwell upon the generality of our results are provided. Moreover, following the fact that most available Ulam-Hyers type stability results deal with crisp mappings, we initiate the study of stability and well-posedness of functional inclusions involving fuzzy set-valued maps. It is well-known that solution of any functional inclusion is a subset of an appropriate ambient space. With this information, fuzzy fixed point problem for which the right-hand-side is a cut set of a fuzzy set-valued map is introduced. Furthermore, sufficient conditions for existence of solutions of Cantilever Beam Problem and integral inclusions are investigated to indicate the usability of our obtained results.

MSC 2010: 46S40; 47H10; 54H25

This work was supported by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under Grant No. (D-546-363-1441). The authors, therefore, gratefully acknowledge the DSR technical and financial support.


  1. (Communicated by Anatolij Dvurečenskij)

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Received: 2020-06-01
Accepted: 2021-03-18
Published Online: 2022-03-28
Published in Print: 2022-04-26

© 2022 Mathematical Institute Slovak Academy of Sciences

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