Approximately generalized additive functions in several variables via fixed point method

Authors

  • S.A.R. Hoseinioun Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701, USA
Abstract:

In this paper, we obtain the general solution and the generalized   Hyers-Ulam-Rassias stability in random normed spaces, in non-Archimedean spaces and also in $p$-Banach spaces and finally the stability via fixed point method for a functional equationbegin{align*}&D_f(x_{1},.., x_{m}):= sum^{m}_{k=2}(sum^{k}_{i_{1}=2}sum^{k+1}_{i_{2}=i_{1}+1}... sum^{m}_{i_{m-k+1}=i_{m-k}+1}) f(sum^{m}_{i=1, ineq i_{1},...,i_{m-k+1} } x_{i}-sum^{m-k+1}_{ r=1} x_{i_{r}})\& hspace {2.8cm}+f(sum^{m}_{ i=1} x_{i})-2^{m-1} f(x_{1})=0end{align*}where $m geq 2$ is an integer number.

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

approximately generalized additive functions in several variables via fixed point method

in this paper, we obtain the general solution and the generalized  hyers--ulam--rassias stability in random normed spaces, in non-archimedean spacesand also in $p$-banach spaces and finally the stability viafixed point method for a functional equationbegin{align*}&d_f(x_{1},.., x_{m}):= sum^{m}_{k=2}(sum^{k}_{i_{1}=2}sum^{k+1}_{i_{2}=i_{1}+1}... sum^{m}_{i_{m-k+1}=i_{m-k}+1}) f(sum^{m}_{i=1...

full text

Approximately generalized additive functions in several variables

The goal of  this paper is to investigate the solutionand stability in random normed spaces, in non--Archimedean spacesand also in $p$--Banach spaces and finally the stability using thealternative fixed point of generalized additive functions inseveral variables.

full text

approximately generalized additive functions in several variables

the goal of  this paper is to investigate the solutionand stability in random normed spaces, in non--archimedean spacesand also in $p$--banach spaces and finally the stability using thealternative fixed point of generalized additive functions inseveral variables.

full text

A New Common Fixed Point Theorem for Suzuki Type Contractions via Generalized $Psi$-simulation Functions

In this paper, a new stratification of mappings, which is  called $Psi$-simulation functions, is introduced  to enhance the study of the Suzuki type weak-contractions. Some well-known results in weak-contractions fixed point theory are generalized by our researches. The methods have been appeared in proving the main results are new and different from the usual methods. Some suitable examples ar...

full text

On the Stability of the Generalized Quadratic and Additive Functional Equation in Random Normed Spaces via Fixed Point Method

In this paper, we prove the stability in random normed spaces via fixed point method for the functional equation f(x+ 2y)− 2f(x+ y) + 2f(x− y)− f(x− 2y) = 0.

full text

Fixed point theorems under weakly contractive conditions via auxiliary functions in ordered $G$-metric spaces

We present some fixed point results for a single mapping and a pair of compatible mappings via auxiliary functions which satisfy a generalized weakly contractive condition in partially ordered complete $G$-metric spaces. Some examples are furnished to illustrate the useability of our main results. At the end, an application is presented to the study of exi...

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}


Journal title

volume 7  issue 1

pages  167- 181

publication date 2016-03-19

By following a journal you will be notified via email when a new issue of this journal is published.

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023