$N$-Jordan $*$-Homomorphisms in $C^{*}$-Algebras

Abstract

In this paper, we investigate n-Jordan * -homomorphisms in C *algebras associated with the following functional inequalityWe moreover prove the superstability and the Hyers-Ulam stability of n-Jordan * -homomorphisms in C * -algebras associated with the following functional equation INTRODUCTION AND PRELIMINARIESLet A,B be complex algebras. A C-linear mapping h : A → B is called an n-Jordan homomorphism if h(a n ) = h(a) n for all a ∈ A. The concept of n-Jordan homomorphisms was studied for complex algebras by Eshaghi Gordji et al. [3] (see also [4,9]).In this paper, assume that n is an integer greater than 1.Definition 1.1. ([10]). Let A, B be complex algebras. A C-linear mapping h :for all a ∈ A.

ADDITIVE Ρ-Functional INEQUALITIES IN Β-Homogeneous F-Spaces

“…Cholewa [5] noticed that the theorem of Skof is still true if the relevant domain 320 Harin Lee, Jae Young Cha, Min Woo Cho & Myungjun Kwon E 1 is replaced by an Abelian group. The stability problems of various functional equations have been extensively investigated by a number of authors (see [1,3,4,6,9,10,11,12,13,15,17,18,19,20,21,24,25]). Definition 1.1.…”

Quadratic rho-functional inequalities in beta-homogeneous normed spaces

“…Cholewa [2] noticed that the theorem of Skof is still true if the relevant domain E 1 is replaced by an Abelian group. The stability problems of various functional equations have been extensively investigated by a number of authors (see [5][6][7][8][11][12][13][14]). (FN 2 ) λx = x for all x ∈ X and all λ with |λ| = 1;…”

STABILITY OF AN ADDITIVE (ρ1, ρ2)-FUNCTIONAL INEQUALITY IN BANACH SPACES

“…Park [18,19] defined additive ρ-functional inequalities and proved the HyersUlam stability of the additive ρ-functional inequalities in Banach spaces and nonArchimedean Banach spaces. The stability problems of various functional equations have been extensively investigated by a number of authors (see [1,3,7,10,17,20,21,24,25,26,27,30,31]). …”