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ADDITIVE (ρ1, ρ2)-FUNCTIONAL INEQUALITIES IN COMPLEX BANACH SPACES.
- Source :
-
Journal of Computational Analysis & Applications . Jan2019, Vol. 26 Issue 1, p367-379. 13p. - Publication Year :
- 2019
-
Abstract
- Abstract. In this paper, we introduce and solve the following additive (ρ1; ρ2)-functional in- equalities ‖ (x + y + z) - f(x) - f(y) - f(z)‖ ≥ kρ,1(f(x + y - z) - f(x) - f(y) + f(z))‖ +‖ρ,2 (f(x - y + z) - f(x) + f(y) - f(z))‖ , (0.1) where ρ1 and ρ,2 are fixed complex numbers with |ρ1| • |ρ,2| > 1, and ‖ (x + y - z) - f(x) - f(y) + f(z)‖ ≥ ‖ρ,1(f(x + y + z) - f(x) - f(y) - f(z))‖ +‖ρ2 (f(x - y + z) - f(x) + f(y) - f(z))‖ (0.2) where ρ,1 and ρ,2 are fixed complex numbers with |ρ1| > 1. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive (ρ1, ρ,2)-functional inequalities (0.1) and (0.2) in complex Banach spaces. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 15211398
- Volume :
- 26
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Computational Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 128999341