scholarly journals THE STABILITY OF FUNCTIONAL INEQUALITIES WITH ADDITIVE MAPPINGS

2009 ◽  
Vol 46 (1) ◽  
pp. 11-23 ◽  
Author(s):  
Young-Sun Cho ◽  
Kil-Woung Jun
Keyword(s):  
Functional Inequalities ◽  
The Stability ◽  
Additive Mappings

On a certain stability of the Hermite–Hadamard inequality

2008 ◽  
Vol 465 (2102) ◽  
pp. 571-583 ◽  
Author(s):  
Attila Házy ◽  
Zsolt Páles
Keyword(s):  
Functional Inequalities ◽  
Hadamard Inequality ◽  
Real Functions ◽  
The Stability

The classical Hermite–Hadamard inequality, under some regularity assumptions, characterizes convexity of real functions. The aim of this paper is to establish connections between the stability forms of the functional inequalities related to Jensen convexity, convexity and the Hermite–Hadamard inequality.

scholarly journals Functional Inequalities Associated with Additive Mappings

2008 ◽  
Vol 2008 ◽  
pp. 1-11 ◽  
Author(s):  
Jaiok Roh ◽  
Ick-Soon Chang
Keyword(s):  
Banach Space ◽  
Functional Inequality ◽  
Functional Inequalities ◽  
Stability Theorems ◽  
Group Divisible ◽  
Additive Mappings

The functional inequality‖f(x)+2f(y)+2f(z)‖≤‖2f(x/2+y+z)‖+ϕ  (x,y,z) (x,y,z∈G)is investigated, whereGis a group divisible by2,f:G→Xandϕ:G3→[0,∞)are mappings, andXis a Banach space. The main result of the paper states that the assumptions above together with (1)ϕ(2x,−x,0)=0=ϕ(0,x,−x) (x∈G)and (2)limn→∞(1/2n)ϕ(2n+1x,2ny,2nz)=0, orlimn→∞2nϕ(x/2n−1,y/2n,z/2n)=0  (x,y,z∈G), imply thatfis additive. In addition, some stability theorems are proved.

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 Stability of Functional Inequalities with Cauchy-Jensen Additive Mappings

2007 ◽  
Vol 2007 ◽  
pp. 1-13 ◽  
Author(s):  
Young-Sun Cho ◽  
Hark-Mahn Kim
Keyword(s):  
Additive Mapping ◽  
Functional Inequalities ◽  
Ulam Stability ◽  
Additive Mappings

We investigate the generalized Hyers-Ulam stability of the functional inequalities associated with Cauchy-Jensen additive mappings. As a result, we obtain that if a mapping satisfies the functional inequalities with perturbation which satisfies certain conditions, then there exists a Cauchy-Jensen additive mapping near the mapping.

scholarly journals Stability of Bi-Additive Mappings and Bi-Jensen Mappings

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1180
Author(s):  
Jae-Hyeong Bae ◽  
Won-Gil Park
Keyword(s):  
Functional Equation ◽  
Stability Problem ◽  
Additive Functional ◽  
Cauchy Equation ◽  
Self Similarity ◽  
Additive Functional Equation ◽  
Jensen Functional Equation ◽  
Jensen Functional ◽  
The Stability ◽  
Additive Mappings

Symmetry is repetitive self-similarity. We proved the stability problem by replicating the well-known Cauchy equation and the well-known Jensen equation into two variables. In this paper, we proved the Hyers-Ulam stability of the bi-additive functional equation f(x+y,z+w)=f(x,z)+f(y,w) and the bi-Jensen functional equation 4fx+y2,z+w2=f(x,z)+f(x,w)+f(y,z)+f(y,w).

scholarly journals Implicit Difference Inequalities Corresponding to First-Order Partial Differential Functional Equations

2009 ◽  
Vol 2009 ◽  
pp. 1-18
Author(s):  
Z. Kamont ◽  
K. Kropielnicka
Keyword(s):  
Functional Equations ◽  
Classical Solutions ◽  
Functional Inequalities ◽  
Partial Differential ◽  
First Order ◽  
Mixed Problems ◽  
Implicit Difference Schemes ◽  
Difference Methods ◽  
The Stability ◽  
Comparison Technique

We give a theorem on implicit difference functional inequalities generated by mixed problems for nonlinear systems of first-order partial differential functional equations. We apply this result in the investigations of the stability of difference methods. Classical solutions of mixed problems are approximated in the paper by solutions of suitable implicit difference schemes. The proof of the convergence of difference method is based on comparison technique, and the result on difference functional inequalities is used. Numerical examples are presented.

Sign in / Sign up

Export Citation Format

Share Document