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AbstractIn this paper, we first investigate the Hyers–Ulam stability of the generalized Cauchy–Jensen functional equation of p-variable f(∑i=1paixi)=∑i=1paif(xi)$f\left(\sum\nolimits_{i = 1}^p {a_i x_i } \right) = \sum\nolimits_{i = 1}^p {a_i f(x_i )}$in an intuitionistic fuzzy Banach space. Then, we conclude the results for Cauchy–Jensen functional equation of p-variable f(x1+⋯+xpp)=1p(f(x1)+⋯+f(xp))$f\left( {{\textstyle{{x_1 + \cdots + x_p } \over p}}} \right) = {1 \over p}(f(x_1 ) + \cdots + f(x_p ))$. Next, we discuss the intuitionistic fuzzy continuity of Cauchy–Jensen mappings.
Demonstratio Mathematica – de Gruyter
Published: Mar 1, 2016
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