Intuitionistic fuzzy almost Cauchy–Jensen mappings

Abstract

In 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.

Keywords

• intuitionistic fuzzy Banach space
• Cauchy–Jensen mapping
• Hyers–Ulam stability
• 34K36
• 46S40
• 47S40
• 39B82
• 39B52
• 26E50