Applying Fixed Point Techniques to Stability Problems in Intuitionistic Fuzzy Banach Spaces

P. Saha, T. K. Samanta, Pratap Mondal, B. S. Choudhury and Manuel De La Sen
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P. Saha: Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, West Bengal 711103, India
T. K. Samanta: Department of Mathematics, Uluberia College, Uluberia, Howrah, West Bengal 711315, India
Pratap Mondal: Department of Mathematics, Bijoy Krishna Girls’ College, Howrah, Howrah, West Bengal 711101, India
B. S. Choudhury: Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, West Bengal 711103, India
Manuel De La Sen: Institute of Research and Development of Processes, Faculty of Science and Technology, University of the Basque Country, Campus of Leioa, Bizkaia, 48940 Leioa, Spain

Mathematics, 2020, vol. 8, issue 6, 1-15

Abstract: In this paper we investigate Hyers-Ulam-Rassias stability of certain nonlinear functional equations. Considerations of such stabilities in different branches of mathematics have been very extensive. Again the fuzzy concepts along with their several extensions have appeared in almost all branches of mathematics. Here we work on intuitionistic fuzzy real Banach spaces, which is obtained by combining together the concepts of fuzzy Banach spaces with intuitionistic fuzzy sets. We establish that pexiderized quadratic functional equations defined on such spaces are stable in the sense of Hyers-Ulam-Rassias stability. We adopt a fixed point approach to the problem. Precisely, we use a generxalized contraction mapping principle. The result is illustrated with an example.

Keywords: Hyers-Ulam stability; pexider type functional equation; intuitionistic fuzzy normed spaces; alternative fixed point theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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