QUADRATIC ρ-FUNCTIONAL INEQUALITIES IN NON-ARCHIMEDEAN NORMED SPACES

초록

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

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