Stability of a mixed type additive-quadratic functional equation with a parameter in matrix intuitionistic fuzzy normed spaces

Zhihua Wang; Zhihua Wang

doi:10.3934/math.20231297

AIMS Mathematics

2023, Volume 8, Issue 11: 25422-25442. doi: 10.3934/math.20231297

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Research article

Stability of a mixed type additive-quadratic functional equation with a parameter in matrix intuitionistic fuzzy normed spaces

Zhihua Wang ^,

School of Science, Hubei University of Technology, Wuhan 430068, China

Received: 19 May 2023 Revised: 09 August 2023 Accepted: 21 August 2023 Published: 31 August 2023
MSC : 39B72, 39B82, 46L07, 47H10

The purpose of this paper is first to introduce the notation of matrix intuitionistic fuzzy normed spaces, and then by virtue of this notation to study the Hyers-Ulam stability results concerning the mixed type additive-quadratic functional equation

$ 2k[f(x+ky)+f(kx+y)] = k(1-s+k+ks+2k^{2})f(x+y)\\+k(1-s-3k+ks+2k^{2})f(x-y) \\ +2kf(kx)+2k(s+k-ks-2k^{2})f(x)+2(1-k-s)f(ky)+2ksf(y)$

in the setting of matrix intuitionistic fuzzy normed spaces by applying two different methods, where $ s $ is a parameter, $ k > 1 $ and $ s\neq 1-2k $. Moreover, the interdisciplinary relation between the theory of matrix intuitionistic fuzzy normed spaces and the theory of functional equations are also presented in this paper.
- fixed point method,
- Hyers-Ulam stability,
- matrix intuitionistic fuzzy normed spaces,
- mixed type additive-quadratic functional equation
Citation: Zhihua Wang. Stability of a mixed type additive-quadratic functional equation with a parameter in matrix intuitionistic fuzzy normed spaces[J]. AIMS Mathematics, 2023, 8(11): 25422-25442. doi: 10.3934/math.20231297

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Abstract

The purpose of this paper is first to introduce the notation of matrix intuitionistic fuzzy normed spaces, and then by virtue of this notation to study the Hyers-Ulam stability results concerning the mixed type additive-quadratic functional equation

$ 2k[f(x+ky)+f(kx+y)] = k(1-s+k+ks+2k^{2})f(x+y)\\+k(1-s-3k+ks+2k^{2})f(x-y) \\ +2kf(kx)+2k(s+k-ks-2k^{2})f(x)+2(1-k-s)f(ky)+2ksf(y)$

in the setting of matrix intuitionistic fuzzy normed spaces by applying two different methods, where $ s $ is a parameter, $ k > 1 $ and $ s\neq 1-2k $. Moreover, the interdisciplinary relation between the theory of matrix intuitionistic fuzzy normed spaces and the theory of functional equations are also presented in this paper.

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