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On a bi-Pexider Functional Equation and its Stability
AIP Conference Proceedings, 2007In this paper, we prove the stability of a bi‐Pexider functional equation f(x+y,z+w) = f1(x,z)+f2(x,w)+f3(y,z)+f4(y,w).
Gwang Hui Kim +5 more
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A wavelike functional equation of Pexider type
Aequationes Mathematicae, 2002A function \(f:G\to H\) is said to be a generalized quadratic polynomial if it can be represented in the form \(f(x)=Q^0+ Q^1(x)+Q^2(x)\), where \(Q^0\) is an arbitrary constant, \(Q^1\) is an additive function and \(Q^2\) is a diagonalization of a symmetric bi-additive function. The first result of this paper is as follows: Let \((G,+)\) and \((H,+)\)
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Pexider generalization of a functional equation of multiplicative symmetry
Publicationes Mathematicae Debrecen, 2004Let \(H\) be a connected subset of \(\mathbb{C}\) such that \(HH \subseteq H\). The author finds and lists the continuous solutions \(F:H \to \mathbb{C}\), \(G:H \to H\) of the functional equation \(F(xG(y)) =F(x)F(y)\), \(x,y \in H\) under various conditions on \(H\).
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On two conditional Pexider functional equations and their stabilities
Nonlinear Analysis: Theory, Methods & Applications, 2009The author solves two conditional Pexider functional equations and investigates their generalized Hyers-Ulam stability. Besides the references given in the paper, the reader can find related results in the book \textit{D. H. Hyers, G. Isac} and \textit{Th. M. Rassias} [Stability of functional equations in several variables.
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On a Class of Functional Equations Which Includes the Pexider's One
Acta Mathematica Hungarica, 2021D Zeglami, B Fadli
exaly
ON SOLUTIONS OF A GENERALIZED QUADRATIC FUNCTIONAL EQUATION OF PEXIDER TYPE
2014In this paper we study general solutions of the following Pexider functional equation (4 − k)f1 Xk i=1 xi + Xk j=2 fj Xk i=1,i6=j xi − xj + fk+1 − x1 + Xk i=2 xi = 4Xk j=1 fk+j+1 xj ,on a vector space over a field of characteristic different from 2, for k ...
JANFADA, Mohammad, SHOURVAZİ, Rahele
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A pexider equation for functions defined on a semigroup
Acta Mathematica Academiae Scientiarum Hungaricae, 1980openaire +1 more source