Applying Fixed Point Techniques to Stability Problems in Intuitionistic Fuzzy Banach Spaces
| Autor: | Tapas Kumar Samanta, Pratap Mondal, P. Saha, Binayak S. Choudhury, Manuel De la Sen |
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| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Mathematics::Functional Analysis
Mathematics::General Mathematics General Mathematics lcsh:Mathematics 010102 general mathematics Stability (learning theory) Banach space Intuitionistic fuzzy 010103 numerical & computational mathematics Fixed point lcsh:QA1-939 01 natural sciences Fuzzy logic pexider type functional equation Algebra Nonlinear system alternative fixed point theorem intuitionistic fuzzy normed spaces Computer Science (miscellaneous) Contraction mapping Hyers-Ulam stability 0101 mathematics Engineering (miscellaneous) Quadratic functional Mathematics |
| Zdroj: | Mathematics, Vol 8, Iss 974, p 974 (2020) Addi. Archivo Digital para la Docencia y la Investigación Universidad de Cantabria (UC) instname Mathematics Volume 8 Issue 6 Pages: 974 Addi: Archivo Digital para la Docencia y la Investigación Universidad del País Vasco |
| Popis: | 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. This work was supported by the Basque Government under the Grant IT 1207-19 |
| Databáze: | OpenAIRE |
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