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Generalized Ulam–Hyers stability of (a, b; k>0)-cubic functional equation in intuitionistic fuzzy normed spaces

Generalized Ulam–Hyers stability of (a, b; k>0)-cubic functional equation in intuitionistic fuzzy... In this paper, we proved the general solution in vector space and established the generalized Ulam–Hyers stability of $$(a,b;k>0)-$$ ( a , b ; k > 0 ) - cubic functional equation $$\begin{aligned} \frac{a+\sqrt{k}~b}{2} f\left( ax+\sqrt{k}~by\right)&+\frac{a-\sqrt{k}~b}{2} f\left( ax-\sqrt{k}~by\right) +k(a^2-kb^2)b^2f(y)\\&=k(ab)^2f(x+y)+(a^2-kb^2)a^2f(x) \end{aligned}$$ a + k b 2 f a x + k b y + a - k b 2 f a x - k b y + k ( a 2 - k b 2 ) b 2 f ( y ) = k ( a b ) 2 f ( x + y ) + ( a 2 - k b 2 ) a 2 f ( x ) where $$a\ne \pm 1, 0; b\ne \pm 1, 0; k>0$$ a ≠ ± 1 , 0 ; b ≠ ± 1 , 0 ; k > 0 in Banach space and Intuitionistic fuzzy normed spaces using both direct and fixed point methods. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Journal of Analysis Springer Journals

Generalized Ulam–Hyers stability of (a, b; k>0)-cubic functional equation in intuitionistic fuzzy normed spaces

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Forum D'Analystes, Chennai
Subject
Mathematics; Analysis; Functional Analysis; Abstract Harmonic Analysis; Special Functions; Fourier Analysis; Measure and Integration
ISSN
0971-3611
eISSN
2367-2501
DOI
10.1007/s41478-018-0083-8
Publisher site
See Article on Publisher Site

Abstract

In this paper, we proved the general solution in vector space and established the generalized Ulam–Hyers stability of $$(a,b;k>0)-$$ ( a , b ; k > 0 ) - cubic functional equation $$\begin{aligned} \frac{a+\sqrt{k}~b}{2} f\left( ax+\sqrt{k}~by\right)&+\frac{a-\sqrt{k}~b}{2} f\left( ax-\sqrt{k}~by\right) +k(a^2-kb^2)b^2f(y)\\&=k(ab)^2f(x+y)+(a^2-kb^2)a^2f(x) \end{aligned}$$ a + k b 2 f a x + k b y + a - k b 2 f a x - k b y + k ( a 2 - k b 2 ) b 2 f ( y ) = k ( a b ) 2 f ( x + y ) + ( a 2 - k b 2 ) a 2 f ( x ) where $$a\ne \pm 1, 0; b\ne \pm 1, 0; k>0$$ a ≠ ± 1 , 0 ; b ≠ ± 1 , 0 ; k > 0 in Banach space and Intuitionistic fuzzy normed spaces using both direct and fixed point methods.

Journal

The Journal of AnalysisSpringer Journals

Published: Jun 8, 2018

References