@article{Wang2023, 
author = {Zhihua Wang},
title = {Stability of a mixed type additive-quadratic functional equation with a parameter in matrix intuitionistic fuzzy normed spaces},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {11},
pages = {25422-25442},
keywords = {fixed point method, Hyers-Ulam stability, matrix intuitionistic fuzzy normed spaces, mixed type additive-quadratic functional equation},
url = {https://www.sciopen.com/article/10.3934/math.20231297},
doi = {10.3934/math.20231297},
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     2  k  [  f  (  x  +  k  y  )  +  f  (  k  x  +  y  )  ]  =  k  (  1  −  s  +  k  +  k  s  +  2      k          2        )  f  (  x  +  y  )    +  k  (  1  −  s  −  3  k  +  k  s  +  2      k          2        )  f  (  x  −  y  )    +  2  k  f  (  k  x  )  +  2  k  (  s  +  k  −  k  s  −  2      k          2        )  f  (  x  )  +  2  (  1  −  k  −  s  )  f  (  k  y  )  +  2  k  s  f  (  y  )in the setting of matrix intuitionistic fuzzy normed spaces by applying two different methods, where    s is a parameter,    k  >  1 and    s  ≠  1  −  2  k. 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.}
}