ADDITIVE-QUADRATIC rho-FUNCTIONAL INEQUALITIES IN beta-HOMOGENEOUS NORMED SPACES

作者：Yun Sungsik; Anastassiou George A; Park Choonkil^*

来源：Journal of Computational Analysis and Applications, 2016, 21(5): 897-909.

• Hyers-Ulam stability
• beta-homogeneous space
• additive-quadratic rho-functional equation
• additive-quadratic rho-functional inequality

In this paper, we solve the following additive-quadratic p-functional inequalities
parallel to f(x + y) + f(x - y) - 2f(x) - f(y) - f(-y)parallel to (0.1)
<= parallel to rho(2f (x + y/2) +2f (x - y/2) -3/2f(x) + 1/2f(x) -1/2f(y) - 1/2f(-y))parallel to,
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) - 3/2f(x) + 1/2f(-x) - 1/2f(y) - 1/2f(-y)parallel to
<=parallel to p(f(x + y) + f(x - y)- 2f(x) - f(y) - f(-y))parallel to,
where rho is a fixed complex number with vertical bar rho vertical bar < 1/2-, and prove the Hyers-Ulam stability of the additive quadratic rho-functional inequalities (0.1) and (0.2) in beta-homogeneous complex Banach spaces and prove the Hyers-Ulam stability of additive-quadratic rho-functional equations associated with the additive-quadratic rho-functional inequalities (0.1) and (0.2) in beta-homogeneous complex Banach spaces.

• 出版日期2016-11