scholarly journals Extension of a generalized Pexider equation

2005 ◽  
Vol 133 (11) ◽  
pp. 3227-3233 ◽  
Author(s):  
János Aczél
Keyword(s):  
Pexider Equation

scholarly journals Some Uniqueness Theorems for Functional Equations

1969 ◽  
Vol 9 (1-2) ◽  
pp. 176-179 ◽  
Author(s):  
T. D. Howroyd
Keyword(s):  
Functional Equations ◽  
Continuous Solution ◽  
Initial Conditions ◽  
Uniqueness Theorems ◽  
Pexider Equation ◽  
Image Position ◽  
Decreasing Functions

The generalized Pexider equation where f and g are unknown and x, y, are real, has been discussed by J. Aczél [1] and J. Aczé and M. Hosszú [2]. In [2] it is shown that if F is continuous and F and H are strictly increasing in their first variables and strictly decreasing in their second variables, then two initial conditions suffice to determine at most one continuous solution f of (1). We extend these results to strictly increasing and strictly decreasing functions F and derive results for strictly monotonic F and H.

scholarly journals Generalized Pexider Equation on an Open Domain

2016 ◽  
Vol 71 (3-4) ◽  
pp. 1359-1372 ◽  
Author(s):  
Małgorzata Chudziak ◽  
Barbara Sobek
Keyword(s):  
Open Domain ◽  
Pexider Equation

Generalized Pexider equation on a restricted domain

2008 ◽  
Vol 52 (6) ◽  
pp. 389-392 ◽  
Author(s):  
Jacek Chudziak ◽  
Józef Tabor
Keyword(s):  
Restricted Domain ◽  
Pexider Equation

Iterative Pexider equation modulo a subset

1997 ◽  
Vol 53 (1-2) ◽  
pp. 155-161
Author(s):  
Mariusz Bajger
Keyword(s):  
Pexider Equation

scholarly journals Connections Between the Completion of Normed Spaces Over Non-Archimedean Fields and the Stability of the Cauchy Equation

2020 ◽  
Vol 34 (1) ◽  
pp. 151-163
Author(s):  
Jens Schwaiger
Keyword(s):  
Banach Spaces ◽  
Normed Space ◽  
Close Connection ◽  
Normed Spaces ◽  
Cauchy Equation ◽  
Absolute Value ◽  
Pexider Equation ◽  
Adic Valuation ◽  
The Stability ◽  
Stability Results

AbstractIn [12] a close connection between stability results for the Cauchy equation and the completion of a normed space over the rationals endowed with the usual absolute value has been investigated. Here similar results are presented when the valuation of the rationals is a p-adic valuation. Moreover a result by Zygfryd Kominek ([5]) on the stability of the Pexider equation is formulated and proved in the context of Banach spaces over the field of p-adic numbers.

scholarly journals On Hyers–Ulam–Rassias Stability of the Pexider Equation

1999 ◽  
Vol 239 (1) ◽  
pp. 20-29 ◽  
Author(s):  
Kil-Woung Jun ◽  
Dong-Soo Shin ◽  
Byung-Do Kim
Keyword(s):  
Pexider Equation ◽  
Rassias Stability

scholarly journals Stability of Pexider Equations on Semigroup with No Neutral Element

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Jaeyoung Chung
Keyword(s):  
Banach Space ◽  
Closed Form ◽  
Direct Consequence ◽  
Neutral Element ◽  
Complex Numbers ◽  
Ulam Stability ◽  
Exponential Equation ◽  
Pexider Equation ◽  
Pexider Equations ◽  
Jung’S Theorem

LetSbe a commutative semigroup with no neutral element,Ya Banach space, andℂthe set of complex numbers. In this paper we prove the Hyers-Ulam stability for Pexider equationfx+y-gx-h(y)≤ϵfor allx,y∈S, wheref,g,h:S→Y. Using Jung’s theorem we obtain a better bound than that usually obtained. Also, generalizing the result of Baker (1980) we prove the superstability for Pexider-exponential equationft+s-gth(s)≤ϵfor allt,s∈S, wheref,g,h:S→ℂ. As a direct consequence of the result we also obtain the general solutions of the Pexider-exponential equationft+s=gth(s)for allt,s∈S, a closed form of which is not yet known.

scholarly journals A fixed points approach to stability of the Pexider equation

2014 ◽  
Vol 7 (2) ◽  
pp. 95-110 ◽  
Author(s):  
B. Bouikhalene ◽  
E. Elqorachi ◽  
J. M. Rassias
Keyword(s):  
Fixed Points ◽  
Pexider Equation
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