Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4663541 | Acta Mathematica Scientia | 2015 | 10 Pages |
Abstract
In this paper, we solve the quadratic ρ-functional inequalities equation(0.1) ‖f(x+y)+f(x−y)−2f(x)−2f(y)‖≤‖ρ(2f(x+y2)+2f(x−y2)−f(x)−f(y))‖,where ρ is a fixed complex number with |ρ| < 1, and equation(0.2) ‖2f(x+y2)+2f(x−y2)−f(x)−f(y)‖≤‖ρ(f(x+y)+f(x−y)−2f(x)−2f(y))‖,where ρ is a fixed complex number with |ρ| < ½.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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Choonkil PARK,