Jensen’s and the quadratic functional equations with an endomorphism [PDF]
Proyecciones (Antofagasta), 2017 We determine the solutions f : S → H of the generalized Jensen’s functional equation f (x + y) + f (x + φ(y)) = 2f (x), x,y ∈ S,and the solutions f : S → H of the generalized quadratic functional equation f (x + y) + f (x + φ(y)) = 2f (x) + 2f (y), x,y ∈ S,where S is a commutative semigroup, H is an abelian group (2-torsion free in the first ...
Sabour, KH, Kabbaj, S
openaire +2 more sources
Stability of generalized quadratic functional equation on a set of measure zero
Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica, 2015 In this paper we prove the Hyers-Ulam stability of the following K-quadratic functional equation ∑ k ∈ K f(x+ k.y)= Lf(x)+ Lf(y), x,y ∈ E, where E is a real (or complex) vector space.
Youssef Aribou +3 more
doaj +1 more source
Nonlinear stability of a quadratic functional equation with complex involution [PDF]
, 2011 summary:Let $X, Y$ be complex vector spaces. Recently, Park and Th.M. Rassias showed that if a mapping $f : X \rightarrow Y$ satisfies \begin{eqnarray} f(x+i y)+ f(x-iy) = 2 f(x) - 2f(y) \end{eqnarray} for all $x$, $y\in X$, then the mapping $f \colon X \
Saadati, Reza, Sadeghi, Ghadir
core +1 more source
Functional inequalities for generalized multi-quadratic mappings
Journal of Inequalities and Applications, 2021 In 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.
Abasalt Bodaghi
doaj +1 more source
Generalized Stability of Euler-Lagrange Quadratic Functional Equation
Abstract and Applied Analysis, 2012 The main goal of this paper is the investigation of the general solution and the generalized Hyers-Ulam stability theorem of the following Euler-Lagrange type quadratic functional equation f(ax+by)+af(x-by)=(a+1)b2f(y)+a(a+1)f(x), in (β,p)-Banach space ...
Hark-Mahn Kim, Min-Young Kim
doaj +1 more source
Quadratic-Quartic Functional Equations in RN-Spaces [PDF]
Journal of Inequalities and Applications, 2009 11 ...
Choonkil Park +2 more
openaire +5 more sources
Asymptotic behaviour of the solution of a functional-differential equation [PDF]
, 1984 The asymptotic behaviour as t→∞ of the solution of the functional- differential equation y'(t) = -y(t/k), with y(0) = 1 and k > 1 , is derived from an integral representation by the method of steepest descents.
Tripp, CE
core +6 more sources
On a functional equation connected with Rao’s quadratic entropy [PDF]
Proceedings of the American Mathematical Society, 1994 We determine the general solution of the functional equation fxy, \[ f (
Chung, J. K. +3 more
openaire +2 more sources
A General Uniqueness Theorem concerning the Stability of Additive and Quadratic Functional Equations
Journal of Function Spaces, 2015 We prove a general uniqueness theorem that can be easily applied to the (generalized) Hyers-Ulam stability of the Cauchy additive functional equation, the quadratic functional equation, and the quadratic-additive type functional equations.
Yang-Hi Lee, Soon-Mo Jung
doaj +1 more source
Fuzzy stability in the sense of Hyers-Ulam-Rassias of a functional equation on quadratic forms
, 2023 We obtain a general solution of the 2-variable quadratic functional equation (formula present) and discuss the stability of the above functional equation, while the quadratic form z(a, b) = aa2 + bab + gc2 is a solution of our functional ...
Jafari, Saeid +4 more
core +1 more source