scholarly journals STABILITY OF AN ADDITIVE FUNCTIONAL INEQUALITY IN BANACH SPACES

2016 ◽  
Vol 29 (1) ◽  
pp. 103-108
Author(s):  
Sang-Cho Chung
Keyword(s):  
Banach Spaces ◽  
Functional Inequality ◽  
Additive Functional ◽  
Additive Functional Inequality

scholarly journals ADDITIVE FUNCTIONAL INEQUALITIES AND DERIVATIONS ON HILBERT C*-MODULES

2013 ◽  
Vol 55 (2) ◽  
pp. 341-348 ◽  
Author(s):  
FRIDOUN MORADLOU
Keyword(s):  
Banach Spaces ◽  
Functional Inequality ◽  
Additive Functional ◽  
Functional Inequalities ◽  
Ulam Stability ◽  
Formula Group ◽  
Image Position

AbstractIn this paper we investigate the following functional inequality $ \begin{eqnarray*} \| f(x-y-z) - f(x-y+z) + f(y) +f(z)\| \leq \|f(x+y-z) - f(x)\| \end{eqnarray*}$ in Banach spaces, and employing the above inequality we prove the generalized Hyers–Ulam stability of derivations in Hilbert C*-modules.

scholarly journals Approximate generalized additive mappings in proper multi-CQ*-algebras

Filomat ◽  
2014 ◽  
Vol 28 (4) ◽  
pp. 677-694 ◽  
Author(s):  
R. Saadati ◽  
Gh. Sadeghi ◽  
Th.M. Rassias
Keyword(s):  
Functional Inequality ◽  
Additive Functional ◽  
Additive Functional Inequality ◽  
Additive Mappings

In this paper, we approximate the following additive functional inequality ?( ?d+1,i=1 f(x1i),..., ?d+1,i=1, f(xki))? ? ?mf (?d+1,i=1 x1i/m),..., mf (?d+1,i=1 xki/m)) ?k for all x11,..., xkd+1?X. We investigate homomorphisms in proper multi-CQ*-algebras and derivations on proper multi-CQ*-algebras associated with the above additive functional inequality.

scholarly journals A fixed point technique for approximate a functional inequality in normed modules over C*-algebras

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1691-1696
Author(s):  
Yeol Cho ◽  
Reza Saadati ◽  
Young-Oh Yang ◽  
H.M. Kenari
Keyword(s):  
Fixed Point ◽  
Error Estimation ◽  
Functional Inequality ◽  
Additive Functional ◽  
C Algebra ◽  
C Algebras ◽  
Additive Functional Inequality ◽  
Fixed Point Technique

In this paper, we apply fixed point technique to investigate the following additive functional inequality: ||f(x)+f(y)+f(z)+f(w)||?||f(x+y)+f(z+w)|| in normed modules over a C*-algebra, which is also applied to understand homomorphisms in C*-algebras. Our results improve and generalize some results given by some authors. Especially, we get a better error estimation of An?s main result.

scholarly journals AN ADDITIVE FUNCTIONAL INEQUALITY

2014 ◽  
Vol 22 (2) ◽  
pp. 317-323
Author(s):  
Sung Jin Lee ◽  
Choonkil Park ◽  
Dong Yun Shin
Keyword(s):  
Functional Inequality ◽  
Additive Functional ◽  
Additive Functional Inequality

scholarly journals Additive ρ-functional inequalities in β-homogeneous normed spaces

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1651-1658
Author(s):  
Choonkil Park
Keyword(s):  
Banach Spaces ◽  
Complex Number ◽  
Functional Equations ◽  
Additive Functional ◽  
Functional Inequalities ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Homogeneous Complex ◽  
Fixed Complex

In this paper, we solve the following additive ?-functional inequalities ||f (x + y) - f (x) - f (y)|| ? ???(2f (x+y/2) - f(x) + -f (y))??, (1) where ? is a fixed complex number with |?|<1, and ??2f(x+y/2)-f(x)- f(y)???||?(f(x+y)-f(x)-f(y))||, (2) where ? is a fixed complex number with |?|<1/2 , and prove the Hyers-Ulam stability of the additive ?-functional inequalities (1) and (2) in ?-homogeneous complex Banach spaces and prove the Hyers-Ulam stability of additive ?-functional equations associated with the additive ?-functional inequalities (1) and (2) in ?-homogeneous complex Banach spaces.

scholarly journals Generalized functional inequalities in Banach spaces

2021 ◽  
Vol 7 (2) ◽  
pp. 337-349
Author(s):  
H. Dimou ◽  
Y. Aribou ◽  
S. Kabbaj
Keyword(s):  
Banach Spaces ◽  
Direct Method ◽  
Additive Functional ◽  
Functional Inequalities ◽  
Ulam Stability

Abstract In this paper, we solve and investigate the generalized additive functional inequalities ‖ F ( ∑ i = 1 n x i ) - ∑ i = 1 n F ( x i ) ‖ ≤ ‖ F ( 1 n ∑ i = 1 n x i ) - 1 n ∑ i = 1 n F ( x i ) ‖ \left\| {F\left( {\sum\limits_{i = 1}^n {{x_i}} } \right) - \sum\limits_{i = 1}^n {F\left( {{x_i}} \right)} } \right\| \le \left\| {F\left( {{1 \over n}\sum\limits_{i = 1}^n {{x_i}} } \right) - {1 \over n}\sum\limits_{i = 1}^n {F\left( {{x_i}} \right)} } \right\| and ‖ F ( 1 n ∑ i = 1 n x i ) - 1 n ∑ i = 1 n F ( x i ) ‖ ≤ ‖ F ( ∑ i = 1 n x i ) - ∑ i = 1 n F ( x i ) ‖ . \left\| {F\left( {{1 \over n}\sum\limits_{i = 1}^n {{x_i}} } \right) - {1 \over n}\sum\limits_{i = 1}^n {F\left( {{x_i}} \right)} } \right\| \le \left\| {F\left( {\sum\limits_{i = 1}^n {{x_i}} } \right) - \sum\limits_{i = 1}^n {F\left( {{x_i}} \right)} } \right\|. Using the direct method, we prove the Hyers-Ulam stability of the functional inequalities (0.1) in Banach spaces and (0.2) in non-Archimedian Banach spaces.

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