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 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 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 On new stability results for composite functional equations in quasi-β-normed spaces

2021 ◽  
Vol 54 (1) ◽  
pp. 68-84
Author(s):  
Anurak Thanyacharoen ◽  
Wutiphol Sintunavarat
Keyword(s):  
Banach Space ◽  
Functional Equation ◽  
Functional Equations ◽  
Direct Method ◽  
Functional Inequality ◽  
Fixed Point Method ◽  
Normed Spaces ◽  
Composite Functional Equations ◽  
Stability Results ◽  
Rassias Stability

Abstract In this article, we prove the generalized Hyers-Ulam-Rassias stability for the following composite functional equation: f ( f ( x ) − f ( y ) ) = f ( x + y ) + f ( x − y ) − f ( x ) − f ( y ) , f(f\left(x)-f(y))=f\left(x+y)+f\left(x-y)-f\left(x)-f(y), where f f maps from a ( β , p ) \left(\beta ,p) -Banach space into itself, by using the fixed point method and the direct method. Also, the generalized Hyers-Ulam-Rassias stability for the composite s s -functional inequality is discussed via our results.

scholarly journals Banach space techniques underpinning a theory for nearly additive mappings

2002 ◽  
Vol 404 ◽  
pp. 1-73 ◽  
Author(s):  
Félix Cabello Sánchez ◽  
Jesús M. F. Castillo
Keyword(s):  
Banach Space ◽  
Additive Mappings

FUNCTIONAL VERSIONS OF SOME REFINED AND REVERSED OPERATOR MEAN INEQUALITIES

2017 ◽  
Vol 96 (3) ◽  
pp. 496-503 ◽  
Author(s):  
MUSTAPHA RAÏSSOULI
Keyword(s):  
Relative Entropy ◽  
Upper Bound ◽  
Functional Inequality ◽  
Arithmetic Mean ◽  
Harmonic Mean ◽  
Functional Inequalities ◽  
Weighted Arithmetic ◽  
Related Operator ◽  
Operator Mean

We present refined and reversed inequalities for the weighted arithmetic mean–harmonic mean functional inequality. Our approach immediately yields the related operator versions in a simple and fast way. We also give some operator and functional inequalities for three or more arguments. As an application, we obtain a refined upper bound for the relative entropy involving functional arguments.

scholarly journals Approximate functional inequalities by additive mappings

2012 ◽  
pp. 461-471
Author(s):  
Hark-Mahn Kim ◽  
Juri Lee ◽  
Eunyoung Son
Keyword(s):  
Functional Inequalities ◽  
Additive Mappings
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