Stability of Functional Inequalities in Banach Algebras

2015 ◽  
pp. 165-199
Author(s):  
Yeol Je Cho ◽  
Choonkil Park ◽  
Themistocles M. Rassias ◽  
Reza Saadati
Keyword(s):  
Banach Algebras ◽  
Functional Inequalities

Bi-additive s-Functional Inequalities and Quasi-∗-Multipliers on Banach ∗-Algebras

2019 ◽  
pp. 199-215
Author(s):  
Jung Rye Lee ◽  
Choonkil Park ◽  
Themistocles M. Rassias
Keyword(s):  
Banach Algebras ◽  
Functional Inequalities

Bi-additive $s$-functional inequalities and quasi-multipliers on Banach algebras

2019 ◽  
Vol 49 (2) ◽  
pp. 593-607 ◽  
Author(s):  
Choonkil Park ◽  
Yuanfeng Jin ◽  
Xiaohong Zhang
Keyword(s):  
Banach Algebras ◽  
Functional Inequalities

scholarly journals Approximate Derivations with the Radical Ranges of Noncommutative Banach Algebras

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Jaiok Roh ◽  
Ick-Soon Chang
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Functional Inequalities ◽  
The Stability

We consider the derivations on noncommutative Banach algebras, and we will first study the conditions for a derivation on noncommutative Banach algebra. Then, we examine the stability of functional inequalities with a derivation. Finally, we take the derivations with the radical ranges on noncommutative Banach algebras.

scholarly journals Biderivations and bihomomorphisms in Banach algebras

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2317-2328 ◽  
Author(s):  
Choonkil Park
Keyword(s):  
Complex Number ◽  
Banach Algebras ◽  
Functional Inequalities ◽  
Ulam Stability ◽  
C Algebras ◽  
Nonzero Complex Number

In this paper, we solve the following bi-additive s-functional inequalities || f(x+y,z+w) + f(x+y,z-w)+f(x-y,z+w) + f (x-y,z-w)- 4f(x,z)||? ||s(2f(x+y,z-w)+ 2f(x-y,z + w)- 4f(x,z) + 4f(y,w)||(1) and ||2f(x+y,z-w) + 2f(x-y,z+w)-4f(x,z) + 4f(y,w)|| (2)? ||s(f(x+y,z+w)+ f(x+y,z-w) + f(x-y,z+w)+f(x-y,z-w)-4f(x,z))||, where s is a fixed nonzero complex number with |s| < 1. Moreover, we prove the Hyers-Ulam stability of biderivations and bihomomorphismsions in Banach algebras and unital C+-algebras, associated with the bi-additive s-functional inequalities (1) and (2).

scholarly journals Hyers–Ulam stability of functional inequalities: a fixed point approach

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Afshan Batool ◽  
Sundas Nawaz ◽  
Ozgur Ege ◽  
Manuel de la Sen
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Banach Algebras ◽  
Fixed Point Method ◽  
Point Method ◽  
Functional Inequalities ◽  
Ulam Stability ◽  
Fixed Point Approach ◽  
Quartic Functional Equation

AbstractUsing the fixed point method, we prove the Hyers–Ulam stability of a cubic and quartic functional equation and of an additive and quartic functional equation in matrix Banach algebras.

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