Stability and hyperstability of orthogonally ∗-m-homomorphisms in orthogonally Lie C∗-algebras: a fixed point approach

Recently Eshaghi et al. introduced orthogonal sets and proved the real generalization of the Banach fixed point theorem on these sets. In this paper, we prove the real generalization of Diaz–Margolis fixed point theorem on orthogonal sets. By using this fixed point theorem, we study the stability of...

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Bibliographic Details
Published inJournal of fixed point theory and applications Vol. 20; no. 2; pp. 1 - 12
Main Authors Bahraini, A., Askari, G., Gordji, M. Eshaghi, Gholami, R.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 2018
Springer Nature B.V
Subjects
Analysis
Fixed points (mathematics)
Functional equations
Homomorphisms
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Stability
Theorems
homomorphisms
39B52
Stability
hyperstability
fixed point approach
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39B82
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Summary:Recently Eshaghi et al. introduced orthogonal sets and proved the real generalization of the Banach fixed point theorem on these sets. In this paper, we prove the real generalization of Diaz–Margolis fixed point theorem on orthogonal sets. By using this fixed point theorem, we study the stability of orthogonally ∗ - m -homomorphisms on Lie C ∗ -algebras associated with the following functional equation: f ( 2 x + y ) + f ( 2 x - y ) + ( m - 1 ) ( m - 2 ) ( m - 3 ) f ( y ) = 2 m - 2 [ f ( x + y ) + f ( x - y ) + 6 f ( x ) ] . for each m = 1 , 2 , 3 , 4 . . Moreover, we establish the hyperstability of these functional equations by suitable control functions.
ISSN:1661-7738
1661-7746
DOI:10.1007/s11784-018-0571-0