scholarly journals A general fixed point method for the stability of the monomial functional equation

2012 ◽  
Vol 28 (1) ◽  
pp. 25-36
Author(s):  
LIVIU CADARIU ◽  
◽  
VIOREL RADU ◽  
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Method ◽  
Point Method ◽  
Normed Spaces ◽  
Jensen Functional Equation ◽  
Jensen Functional ◽  
Error Estimations ◽  
The Stability ◽  
Stability Results

In this paper, we extend the ideas in [Cadariu, L. and Radu, V., ˘ A general fixed point method for the stability of Jensen functional equation, Bull. S¸ t. Univ. Politehnica Timis¸oara, Ser. Mat.-Fiz. 51(65) (2006), No. 2, 63–72] to obtain some general stability results for monomial functional equations in β−normed spaces. The fixed point alternative together the error estimations for generalized contractions of type Bianchini-Grandolfi are pointed out, and then used as fundamental tool. Some applications and examples which emphasize the very general hypotheses, are also given.

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 On the Stability of an -Variables Functional Equation in Random Normed Spaces via Fixed Point Method

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
A. Ebadian ◽  
M. Eshaghi Gordji ◽  
H. Khodaei ◽  
R. Saadati ◽  
Gh. Sadeghi
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Method ◽  
Point Method ◽  
Integer Number ◽  
Normed Spaces ◽  
Random Normed Spaces ◽  
The Stability ◽  
Rassias Stability

At first we find the solution of the functional equation where is an integer number. Then, we obtain the generalized Hyers-Ulam-Rassias stability in random normed spaces via the fixed point method for the above functional equation.

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