Non-Archimedean stability of a generalized reciprocal-quadratic functional equation in several variables by direct and fixed point methods

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3199-3209
Author(s):  
Senthil Kumar ◽  
Hemen Dutta
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Several Variables ◽  
Fixed Point Methods

Non-Archimedean stability of a generalized reciprocal-quadratic functional equation in several variables by direct and fixed point methods

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3199-3209 ◽  
Author(s):  
Senthil Kumar ◽  
Hemen Dutta
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Real Numbers ◽  
Several Variables ◽  
Fixed Point Methods

This study is aimed to determine various stabilities of a generalized reciprocal-quadratic functional equation of the form r (?pj=1 ?juj) = ?pj=1 r (uj) [?pj=1 ?j ?pk=1,k?j ?r(uk)] 2 connected with Ulam, Hyers, T. M. Rassias, J. M. Rassias and Gavruta in non-Archimedean fields, where ?j?0; j = 1,2,..., p are arbitrary real numbers and 0 < ?1+?2+...+?p = ?pj=1 ?j=??1 in non-Archimedean fields by direct and fixed point methods.

scholarly journals General solution and generalized Ulam-Hyers stability of a generalized n- type additive quadratic functional equation in Banach space and Banach algebra: direct and fixed point methods

2015 ◽  
Vol 3 (1) ◽  
pp. 25
Author(s):  
S. Murthy ◽  
M. Arunkumar ◽  
V. Govindan
Keyword(s):  
Banach Space ◽  
Functional Equation ◽  
Fixed Point ◽  
Positive Integer ◽  
General Solution ◽  
Banach Algebra ◽  
Banach Algebras ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Fixed Point Methods

<p>In this paper, the authors introduce and investigate the general solution and generalized Ulam-Hyers stability of a generalized <em>n</em>-type additive-quadratic functional equation.</p><p><br />g(x + 2y; u + 2v) + g(x 􀀀 2y; u 􀀀 2v) = 4[g(x + y; u + v) + g(x 􀀀 y; u 􀀀 v)] 􀀀 6g(x; u)<br />+ g(2y; 2v) + g(􀀀2y;􀀀2v) 􀀀 4g(y; v) 􀀀 4g(􀀀y;􀀀v)</p><p>Where  is a positive integer with , in Banach Space and Banach Algebras using direct and fixed point methods.</p>

scholarly journals Stability of ann-Dimensional Mixed-Type Additive and Quadratic Functional Equation in Random Normed Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Yang-Hi Lee ◽  
Soon-Mo Jung
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Mixed Type ◽  
Fixed Point Method ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Normed Spaces ◽  
Stability Problems ◽  
Random Normed Spaces ◽  
The Stability

We investigate the stability problems for then-dimensional mixed-type additive and quadratic functional equation2f(∑j=1nxj)+∑1≤i,j≤n,  i≠jf(xi-xj)=(n+1)∑j=1nf(xj)+(n-1)∑j=1nf(-xj)in random normed spaces by applying the fixed point method.

scholarly journals A New Fixed Point Theorem and a New Generalized Hyers-Ulam-Rassias Stability in Incomplete Normed Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1117
Author(s):  
Maryam Ramezani ◽  
Ozgur Ege ◽  
Manuel De la Sen
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Fixed Point Method ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Normed Spaces ◽  
Rassias Stability

In this study, our goal is to apply a new fixed point method to prove the Hyers-Ulam-Rassias stability of a quadratic functional equation in normed spaces which are not necessarily Banach spaces. The results of the present paper improve and extend some previous results.

Sign in / Sign up

Export Citation Format

Share Document