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 On alienation of two functional equations of quadratic type

2021 ◽  
Author(s):  
Roman Ger
Keyword(s):  
Functional Equation ◽  
Functional Equations ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Real Numbers ◽  
Alpha Beta ◽  
Beta 2 ◽  
Special Case

Abstract  We deal with an alienation problem for an Euler–Lagrange type functional equation $$\begin{aligned} f(\alpha x + \beta y) + f(\alpha x - \beta y) = 2\alpha ^2f(x) + 2\beta ^2f(y) \end{aligned}$$ f ( α x + β y ) + f ( α x - β y ) = 2 α 2 f ( x ) + 2 β 2 f ( y ) assumed for fixed nonzero real numbers $$\alpha ,\beta ,\, 1 \ne \alpha ^2 \ne \beta ^2$$ α , β , 1 ≠ α 2 ≠ β 2 , and the classic quadratic functional equation $$\begin{aligned} g(x+y) + g(x-y) = 2g(x) + 2g(y). \end{aligned}$$ g ( x + y ) + g ( x - y ) = 2 g ( x ) + 2 g ( y ) . We were inspired by papers of Kim et al. (Abstract and applied analysis, vol. 2013, Hindawi Publishing Corporation, 2013) and Gordji and Khodaei (Abstract and applied analysis, vol. 2009, Hindawi Publishing Corporation, 2009), where the special case $$g = \gamma f$$ g = γ f was examined.

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.

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