scholarly journals Nearly Quadratic Mappings overp-Adic Fields

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
M. Eshaghi Gordji ◽  
H. Khodaei ◽  
Gwang Hui Kim
Keyword(s):  
Functional Equation ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Quadratic Mappings ◽  
Stability Results

We establish some stability results overp-adic fields for the generalized quadratic functional equation∑k=2n∑i1=2k∑i2=i1+1k+1⋯∑in-k+1=in-k+1nf(∑i=1,i≠i1,…,in-k+1nxi-∑r=1n-k+1xir)+f(∑i=1nxi)=2n-1∑i=1nf(xi),wheren∈Nandn≥2.

scholarly journals Ulam Type Stability of ?-Quadratic Mappings in Fuzzy Modular ∗-Algebras

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1630
Author(s):  
Hark-Mahn Kim ◽  
Hwan-Yong Shin
Keyword(s):  
Functional Equation ◽  
Lower Semicontinuity ◽  
Product Space ◽  
Quadratic Functional Equation ◽  
Inner Product ◽  
Quadratic Functional ◽  
Quadratic Mappings ◽  
The Stability ◽  
Ulam Type Stability ◽  
Stability Results

In this paper, we find the solution of the following quadratic functional equation n∑1≤i<j≤nQxi−xj=∑i=1nQ∑j≠ixj−(n−1)xi, which is derived from the gravity of the n distinct vectors x1,⋯,xn in an inner product space, and prove that the stability results of the A-quadratic mappings in μ-complete convex fuzzy modular ∗-algebras without using lower semicontinuity and β-homogeneous property.

scholarly journals Generalized Stability ofC*-Ternary Quadratic Mappings

2007 ◽  
Vol 2007 ◽  
pp. 1-6 ◽  
Author(s):  
Choonkil Park ◽  
Jianlian Cui
Keyword(s):  
Functional Equation ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Quadratic Mappings ◽  
Generalized Stability

We prove the generalized stability ofC*-ternary quadratic mappings inC*-ternary rings for the quadratic functional equationf(x+y)+f(x−y)=2f(x)+2f(y).

scholarly journals Hyers-Ulam Stability of Quadratic Functional Equation Based on Fixed Point Technique in Banach Spaces and Non-Archimedean Banach Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2575
Author(s):  
Kandhasamy Tamilvanan ◽  
Abdulaziz M. Alanazi ◽  
Maryam Gharamah Alshehri ◽  
Jeevan Kafle
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Fixed Point Technique ◽  
Fixed Point Techniques ◽  
Stability Results

In this paper, the authors investigate the Hyers–Ulam stability results of the quadratic functional equation in Banach spaces and non-Archimedean Banach spaces by utilizing two different techniques in terms of direct and fixed point techniques.

scholarly journals Ulam Stabilities and Instabilities of Euler–Lagrange-Rassias Quadratic Functional Equation in Non-Archimedean IFN spaces

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3063
Author(s):  
Kandhasamy Tamilvanan ◽  
Abdulaziz Mohammed Alanazi ◽  
John Michael Rassias ◽  
Ali H. Alkhaldi
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Quadratic Mapping ◽  
Normed Spaces ◽  
Intuitionistic Fuzzy ◽  
Fixed Point Techniques ◽  
Intuitionistic Fuzzy Normed Spaces ◽  
Stability Results

In this paper, we use direct and fixed-point techniques to examine the generalised Ulam–Hyers stability results of the general Euler–Lagrange quadratic mapping in non-Archimedean IFN spaces (briefly, non-Archimedean Intuitionistic Fuzzy Normed spaces) over a field.

scholarly journals Functional inequalities for generalized multi-quadratic mappings

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Abasalt Bodaghi
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Functional Equations ◽  
Single Equation ◽  
Quadratic Functional ◽  
Functional Inequalities ◽  
Ulam Stability ◽  
Several Variables ◽  
Quadratic Mappings ◽  
Stability Results

AbstractIn this article, we introduce some special several variables mappings which are quadratic in each variable and show that such mappings can be defined as a single equation that is the generalized multi-quadratic functional equation. We also apply a fixed point theorem to establish the Hyers–Ulam stability for the generalized multi-quadratic functional equations. Furthermore, we present an example and a few corollaries corresponding to some known stability results.

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.

Projective actions, invariant sigma-curves and quadratic functional equations

1985 ◽  
Vol 98 (2) ◽  
pp. 195-212 ◽  
Author(s):  
Patrick J. McCarthy
Keyword(s):  
Functional Equation ◽  
Periodic Function ◽  
Functional Equations ◽  
Continuous Solution ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Continuous Solutions ◽  
Linear Map

AbstractThe quadratic functional equation f(f(x)) *–Tf(x) + Dx = 0 is equivalent to the requirement that the graph be invariant under a certain linear map The induced projective map is used to show that the equation admits a rich supply of continuous solutions only when L is hyperbolic (T2 > 4D), and then only when T and D satisfy certain further conditions. The general continuous solution of the equation is given explicitly in terms of either (a) an expression involving an arbitrary periodic function, function additions, inverses and composites, or(b) suitable limits of such solutions.

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