Additive rho-Functional Inequalities in beta-Homogeneous Normed Spaces

作者：Park Choonkil^*

来源：Filomat, 2016, 30(7): 1651-1658.

DOI：10.2298/FIL1607651P

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

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

• 出版日期2016