Abstract and Applied Analysis

Ulam’s Type Stability of Involutional-Exponential Functional Equations

Jaeyoung Chung

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Abstract

Let S be a commutative semigroup, f , g : S C and σ : S S an involution. In this paper we consider the stability of involution-exponential functional equations f x + σ y - g x f y ϕ x resp .,    ϕ y ,   | f ( x + σ y ) - f ( x ) g ( y ) | ϕ ( x )   [ resp .,    ϕ ( y ) ] for all x , y S , where ϕ : S R + satisfies the growth condition: there exists C > 1 such that lim k C - k ϕ ( k x ) = 0 for each x S . We also consider the stability of L -version | f ( x + σ y ) - f ( x ) f ( y ) | L ( R 2 n ) ϵ , where f : R n C is a locally integrable function.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 763914, 9 pages.

Dates
First available in Project Euclid: 27 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1425049820

Digital Object Identifier
doi:10.1155/2014/763914

Mathematical Reviews number (MathSciNet)
MR3272212

Zentralblatt MATH identifier
07023038

Citation

Chung, Jaeyoung. Ulam’s Type Stability of Involutional-Exponential Functional Equations. Abstr. Appl. Anal. 2014 (2014), Article ID 763914, 9 pages. doi:10.1155/2014/763914. https://projecteuclid.org/euclid.aaa/1425049820


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