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Intuitionistic fuzzy almost Cauchy–Jensen mappings

Intuitionistic fuzzy almost Cauchy–Jensen mappings 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

Intuitionistic fuzzy almost Cauchy–Jensen mappings

Demonstratio Mathematica , Volume 49 (1): 8 – Mar 1, 2016

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References (12)

Publisher
de Gruyter
Copyright
© 2016 M. E. Gordji et al., published by De Gruyter Open
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-2016-0003
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Demonstratio Mathematicade Gruyter

Published: Mar 1, 2016

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