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Quadratic rho-functional inequalities in Banach spaces

Title
Quadratic rho-functional inequalities in Banach spaces
Author
Keywords
Hyers-Ulam stability; quadratic ρ-functional equation; fixed point; complex Banach space
Issue Date
2015-07
Publisher
강원경기수학회
Citation
한국수학논문집, v. 23, NO 2, Page. 231-248
Abstract
In this paper, we solve the following quadratic $\rho$-functional inequalities ∥ ∥ ∥ f(x+y+z2 )+f(x−y−z2 )+f(y−x−z2 )+f(z−x−y2 )−f(x)−f(y)−f(z)∥ ∥ ∥ ≤∥ρ(f(x+y+z)+f(x−y−z)+f(y−x−z) +f(z−x−y)−4f(x)−4f(y)−4f(z))∥, ‖f(x+y+z2)+f(x−y−z2)+f(y−x−z2)+f(z−x−y2)−f(x)−f(y)−f(z)‖≤‖ρ(f(x+y+z)+f(x−y−z)+f(y−x−z) +f(z−x−y)−4f(x)−4f(y)−4f(z))‖, where $\rho$ is a fixed complex number with $|\rho|<\frac{1}{8}$, and ∥f(x+y+z)+f(x−y−z)+f(y−x−z)+f(z−x−y)−4f(x)−4f(y)−4f(z)∥≤∥ ∥ ∥ ρ(f(x+y+z2 )+f(x−y−z2 )+f(y−x−z2 )+f(z−x−y2 )−f(x)−f(y)−f(z))∥ ∥ ∥ , ‖f(x+y+z)+f(x−y−z)+f(y−x−z)+f(z−x−y)−4f(x)−4f(y)−4f(z)‖≤‖ρ(f(x+y+z2)+f(x−y−z2)+f(y−x−z2)+f(z−x−y2)−f(x)−f(y)−f(z))‖, where $\rho$ is a fixed complex number with $|\rho|<4$. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic $\rho$-functional inequalities (0.1) and (0.2) in complex Banach spaces.
URI
http://kkms.org/index.php/kjm/article/view/374http://hdl.handle.net/20.500.11754/26578
ISSN
1976-8605; 2288-1433
DOI
10.11568/kjm.2015.23.2.231
Appears in Collections:
COLLEGE OF NATURAL SCIENCES[S](자연과학대학) > MATHEMATICS(수학과) > Articles
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