scholarly journals STABILITY OF DRYGAS TYPE FUNCTIONAL EQUATIONS WITH INVOLUTION IN NON-ARCHIMEDEAN BANACH SPACES BY FIXED POINT METHOD

2016 ◽  
Vol 34 (5_6) ◽  
pp. 509-517
Author(s):  
CHANG IL KIM ◽  
GIL JUN HAN
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Functional Equations ◽  
Fixed Point Method ◽  
Point Method

scholarly journals Ulam stability of functional equations in 2-Banach spaces via the fixed point method

2021 ◽  
Vol 23 (3) ◽  
Author(s):  
Krzysztof Ciepliński
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Functional Equations ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Several Variables ◽  
Stability Of Functional Equations ◽  
Special Cases ◽  
The Stability

AbstractUsing the fixed point method, we prove the Ulam stability of two general functional equations in several variables in 2-Banach spaces. As corollaries from our main results, some outcomes on the stability of a few known equations being special cases of the considered ones will be presented. In particular, we extend several recent results on the Ulam stability of functional equations in 2-Banach spaces.

scholarly journals Approximately Quintic and Sextic Mappings Formr-Divisible Groups into Ŝerstnev Probabilistic Banach Spaces: Fixed Point Method

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
M. Eshaghi Gordji ◽  
Y. J. Cho ◽  
M. B. Ghaemi ◽  
H. Majani
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Functional Equations ◽  
Fixed Point Method ◽  
Point Method ◽  
Constant Coefficients ◽  
The Stability ◽  
Divisible Groups

Using the fixed point method, we investigate the stability of the systems of quadratic-cubic and additive-quadratic-cubic functional equations with constant coefficients formr-divisible groups into Ŝerstnev probabilistic Banach spaces.

scholarly journals Fixed Points and the Stability of an AQCQ-Functional Equation in Non-Archimedean Normed Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Choonkil Park
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Quartic Functional Equation ◽  
The Stability

Using fixed point method, we prove the generalized Hyers-Ulam stability of the following additive-quadratic-cubic-quartic functional equationf(x+2y)+f(x−2y)=4f(x+y)+4f(x−y)−6f(x)+f(2y)+f(−2y)−4f(y)−4f(−y)in non-Archimedean Banach spaces.

scholarly journals Brzdęk’s fixed point method for the generalised hyperstability of bi-Jensen functional equation in (2,β)-Banach spaces

Filomat ◽  
2018 ◽  
Vol 32 (14) ◽  
pp. 4897-4910
Author(s):  
Iz-Iddine El-Fassi
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Fixed Point Method ◽  
Point Method ◽  
Jensen Functional Equation ◽  
Jensen Functional ◽  
The Fixed Point Theorem

Using the fixed point theorem [12, Theorem 1] in (2,?)-Banach spaces, we prove the generalized hyperstability results of the bi-Jensen functional equation 4f(x + z/2; y + w/2) = f (x,y) + f (x,w) + f (z,y) + f (y,w). Our main results state that, under some weak natural assumptions, functions satisfying the equation approximately (in some sense) must be actually solutions to it. The method we use here can be applied to various similar equations in many variables.

scholarly journals The Stability of a Quadratic Functional Equation with the Fixed Point Alternative

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Choonkil Park ◽  
Ji-Hye Kim
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Method ◽  
Point Method ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
The Stability

Lee, An and Park introduced the quadratic functional equationf(2x+y)+f(2x−y)=8f(x)+2f(y)and proved the stability of the quadratic functional equation in the spirit of Hyers, Ulam and Th. M. Rassias. Using the fixed point method, we prove the generalized Hyers-Ulam stability of the quadratic functional equation in Banach spaces.

scholarly journals Stability of a Quartic Functional Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Abasalt Bodaghi
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Positive Integer ◽  
General Solution ◽  
Banach Spaces ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Quartic Functional Equation ◽  
Fixed Positive Integer

We obtain the general solution of the generalized quartic functional equationf(x+my)+f(x-my)=2(7m-9)(m-1)f(x)+2m2(m2-1)f(y)-(m-1)2f(2x)+m2{f(x+y)+f(x-y)}for a fixed positive integerm. We prove the Hyers-Ulam stability for this quartic functional equation by the directed method and the fixed point method on real Banach spaces. We also investigate the Hyers-Ulam stability for the mentioned quartic functional equation in non-Archimedean spaces.

scholarly journals Generalized Hyers-Ulam stability for general additive functional equations on non-Archimedean random lie C*-algebras

Filomat ◽  
2018 ◽  
Vol 32 (6) ◽  
pp. 2127-2138
Author(s):  
Zhihua Wang ◽  
Prasanna Sahoo
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Functional Equations ◽  
Additive Functional ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Fixed Integer ◽  
Additive Functional Equation ◽  
C Algebras

In this paper, using the fixed point method, we prove some results related to the generalized Hyers-Ulam stability of homomorphisms and derivations in non-Archimedean random C*-algebras and non-Archimedean random Lie C*-algebras for the generalized additive functional equation ?1 ? i < j ?n f(xi+xj/2 + ?n-2 l=1,kl?i,j xkl) = (n-1)2/2 ?n,i=1 f(xi) where n ? N is a fixed integer with n ? 3.

scholarly journals Generalized Hyers-Ulam stability of cubic functional inequality

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1969-1978
Author(s):  
Hark-Mahn Kim ◽  
Eunyoung Son
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Direct Method ◽  
Functional Inequality ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability

In this article, we investigate the generalized Hyers-Ulam stability of a cubic functional inequality in Banach spaces and in non-Archimedean Banach spaces by using fixed point method and direct method, respectively.

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