Additive rho-functional inequalities

作者：Park Choonkil^*

来源：Journal of Nonlinear Sciences and Applications, 2014, 7(5): 296-310.

DOI：10.22436/jnsa.007.05.02

• Hyers-Ulam stability
• additive rho-functional equation
• additive rho-functional inequality
• non-Archimedean normed space
• Banach space

In this paper, we solve the 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)
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 non-Archimedean number with vertical bar rho vertical bar < 1 or rho is a fixed complex number with vertical bar rho vertical bar < 1. Using the direct method, we prove the Hyers-Ulam stability of the additive rho-functional inequalities (I) and (2) in non-Archimedean Banach spaces and in 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 non-Archimedean Banach spaces and in complex Banach spaces.

• 出版日期2014