Additive ๐บ-functional inequalities
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In this paper, we solve the additive ๐บ-functional inequalities |f(x+y)+ f(x-y)-2f(x)| < | ๐บ (2 f({x+y}/{2}) + f(x-y )- 2f(x) ) |, ---(0.1) where ๐บ is a fixed complex number with |rho|<1, and |2 f({x+y}/{2}) + f(x-y)- 2 f(x) | < |๐บ(f(x+y)+f(x-y)-2f(x)) | , ---(0.2) where ๐บ is a fixed complex number with |rho|<1. Furthermore, we prove the Hyers-Ulam stability of the additive ๐บ-functional inequalities (0.1) and (0.2) in complex Banach spaces.
Abstract
In this paper, we solve the additive ๐บ-functional inequalities |f(x+y)+ f(x-y)-2f(x)| < | ๐บ (2 f({x+y}/{2}) + f(x-y )- 2f(x) ) |, ---(0.1) where ๐บ is a fixed complex number with |rho|<1, and |2 f({x+y}/{2}) + f(x-y)- 2 f(x) | < |๐บ(f(x+y)+f(x-y)-2f(x)) | , ---(0.2) where ๐บ is a fixed complex number with |rho|<1. Furthermore, we prove the Hyers-Ulam stability of the additive ๐บ-functional inequalities (0.1) and (0.2) in complex Banach spaces.
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