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Search Results (4)

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Keywords = stability intuitionistic fuzzy normed spaces

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11 pages, 289 KB  
Article
Hyers Stability in Generalized Intuitionistic P-Pseudo Fuzzy 2-Normed Spaces
by Ehsan Movahednia and Manuel De la Sen
Axioms 2023, 12(1), 28; https://doi.org/10.3390/axioms12010028 - 26 Dec 2022
Cited by 1 | Viewed by 1897
Abstract
In this article, we defined the generalized intuitionistic P-pseudo fuzzy 2-normed spaces and investigated the Hyers stability of m-mappings in this space. The m-mappings are interesting functional equations; these functional equations are additive for m = 1, quadratic for m = [...] Read more.
In this article, we defined the generalized intuitionistic P-pseudo fuzzy 2-normed spaces and investigated the Hyers stability of m-mappings in this space. The m-mappings are interesting functional equations; these functional equations are additive for m = 1, quadratic for m = 2, cubic for m = 3, and quartic for m = 4. We have investigated the stability of four types of functional equations in generalized intuitionistic P-pseudo fuzzy 2-normed spaces by the fixed point method. Full article
(This article belongs to the Special Issue 10th Anniversary of Axioms: Mathematical Analysis)
24 pages, 337 KB  
Article
Intuitionistic Fuzzy Stability of an Euler–Lagrange Symmetry Additive Functional Equation via Direct and Fixed Point Technique (FPT)
by P. Agilan, K. Julietraja, Nabil Mlaiki and Aiman Mukheimer
Symmetry 2022, 14(11), 2454; https://doi.org/10.3390/sym14112454 - 19 Nov 2022
Cited by 11 | Viewed by 1767
Abstract
In this article, a new class of real-valued Euler–Lagrange symmetry additive functional equations is introduced. The solution of the equation is provided, assuming the unknown function to be continuous and without any regularity conditions. The objective of this research is to derive the [...] Read more.
In this article, a new class of real-valued Euler–Lagrange symmetry additive functional equations is introduced. The solution of the equation is provided, assuming the unknown function to be continuous and without any regularity conditions. The objective of this research is to derive the Hyers–Ulam–Rassias stability (HURS) in intuitionistic fuzzy normed spaces (IFNS) by applying the classical direct method and fixed point techniques (FPT). Furthermore, it is proven that the Euler–Lagrange symmetry additive functional equation and the control function, which is the IFNS of the sums and products of powers of norms, is stable. In addition, a few examples where the solution of this equation can be applied in Fourier series and Fourier transforms are demonstrated. Full article
(This article belongs to the Section Mathematics)
16 pages, 316 KB  
Article
Ulam Stabilities and Instabilities of Euler–Lagrange-Rassias Quadratic Functional Equation in Non-Archimedean IFN Spaces
by Kandhasamy Tamilvanan, Abdulaziz Mohammed Alanazi, John Michael Rassias and Ali H. Alkhaldi
Mathematics 2021, 9(23), 3063; https://doi.org/10.3390/math9233063 - 28 Nov 2021
Cited by 5 | Viewed by 2254
Abstract
In this paper, we use direct and fixed-point techniques to examine the generalised Ulam–Hyers stability results of the general Euler–Lagrange quadratic mapping in non-Archimedean IFN spaces (briefly, non-Archimedean Intuitionistic Fuzzy Normed spaces) over a field. Full article
(This article belongs to the Special Issue Advances in Functional Equations and Convex Analysis)
15 pages, 272 KB  
Article
Applying Fixed Point Techniques to Stability Problems in Intuitionistic Fuzzy Banach Spaces
by P. Saha, T. K. Samanta, Pratap Mondal, B. S. Choudhury and Manuel De La Sen
Mathematics 2020, 8(6), 974; https://doi.org/10.3390/math8060974 - 15 Jun 2020
Cited by 10 | Viewed by 2392
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications 2020)
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