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 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 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 On the non-Archimedean and random approximately general additive mappings: Direct and fixed point methods

Filomat ◽  
2014 ◽  
Vol 28 (9) ◽  
pp. 1753-1771
Author(s):  
Azadi Kenary ◽  
M.H. Eghtesadifard
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Positive Integer ◽  
Additive Functional ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Additive Functional Equation ◽  
Fixed Point Methods ◽  
Additive Mappings

In this paper, we prove the Hyers-Ulam stability of the following generalized additive functional equation ?1? i < j ? m f(xi+xj/2 + m-2?l=1,kl?i,j) = (m-1)2/2 m?i=1 f(xi) where m is a positive integer greater than 3, in various normed spaces.

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