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QUADRATIC ρ-FUNCTIONAL INEQUALITIES IN BANACH SPACES.
- Source :
-
Journal of Computational Analysis & Applications . May2019, Vol. 26 Issue 5, p863-874. 12p. - Publication Year :
- 2019
-
Abstract
- In this paper, we solve the following quadratic ρ-functional inequalities ‖f (x + y + z/2) + f(x - y - z/2) + f(y - x - z/2) + f(z - x - y/2) -f(x) - f(y) - f(z)‖ ≤ ‖ρ(f(x + y + z) + f(x - y - z) + f(y - x - z) + f(z - x - y) (0.1) -4f(x) - 4f(y) - 4f(z))‖; where ρ is a fixed complex number with |ρ| < 1/8, and ‖f(x + y + z) + f(x - y - z) + f(y - x - z) + f(z - x - y) -4f(x) - 4f(y) - 4f(z)‖ (0.2) ≤ ‖ ρ(f(x + y + z/2) + f(x - y - z/2) + f(y - x - z/2) + f(z - x - y/2) -f(x) - f(y) - f(z))‖ ; where ρ is a fixed complex number with |ρ| < 4. Using the direct method, we prove the Hyers-Ulam stability of the quadratic ρ-functional inequalities (0.1) and (0.2) in complex Banach spaces and prove the Hyers-Ulam stability of quadratic ρ-functional equations associated with the quadratic ρ-functional inequalities (0.1) and (0.2) in complex Banach spaces. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 15211398
- Volume :
- 26
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Journal of Computational Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 129613101