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QUADRATIC rho-FUNCTIONAL INEQUALITIES IN BANACH SPACES

Title
QUADRATIC rho-FUNCTIONAL INEQUALITIES IN BANACH SPACES
Author
박춘길
Keywords
Hyers-Ulam stability; quadratic rho-functional equation; quadratic rho-functional inequality; complex Banach space
Issue Date
2015-11
Publisher
ELSEVIER SCIENCE INC
Citation
ACTA MATHEMATICA SCIENTIA, v. 35, NO 6, Page. 1501-1510
Abstract
In this paper, we solve the quadratic rho-functional inequalities parallel to f(x + y) + f(x - y) - 2f(x) - 2f(y)parallel to ˂= parallel to rho(2f (x+y/2) + 2f (x - y/2) - f(x) - f(y))parallel to, (0.1) where rho is a fixed complex number with vertical bar rho vertical bar ˂ 1, and parallel to 2f (x + y/2) + 2f(x - y/2) - f(x) - f(y)parallel to ˂=parallel to rho(f(x + y) + f(x - y) - 2f(x) - 2f(y))parallel to, (0.2) where rho is a fixed complex number with vertical bar rho vertical bar ˂ 1/2. Using the direct method, we prove the Hyers-Ulam stability of the quadratic rho-functional inequalities (0.1) and (0.2) in complex Banach spaces and prove the Hyers-Ulam stability of quadratic rho-functional equations associated with the quadratic rho-functional inequalities (0.1) and (0.2) in complex Banach spaces.
URI
http://www.sciencedirect.com/science/article/pii/S0252960215300710?via%3Dihubhttp://hdl.handle.net/20.500.11754/29104
ISSN
0252-9602; 1572-9087
DOI
10.1016/S0252-9602(15)30071-0
Appears in Collections:
COLLEGE OF NATURAL SCIENCES[S](자연과학대학) > MATHEMATICS(수학과) > Articles
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