QUADRATIC ρ-FUNCTIONAL INEQUALITIES IN NON-ARCHIMEDEAN BANACH SPACES.

In this paper, we solve the quadratic ρ-functional inequalities ‖f(x + y) + f(x - y) - 2f(x) - 2f(y)‖ ≤ ‖ρ(4f (x + y/2) + f (x - y) - 2f (x) - 2f (y)) ‖, where ρ is a fixed non-Archimedean number with ∣ρ∣ < ∣2∣, and ‖4f (x + y/2) + f (x - y) - 2f (x) - 2f(y) ‖ ≤ ‖ρ(f(x + y) + f(x - y) - 2f (x) - 2f (y))‖, where ρ is a fixed non-Archimedean number with ∣ρ∣ < 1. Furthermore, we prove the Hyers-Ulam stability of the quadratic p-functional inequalities (0.1) and (0.2) in non-Archimedean Banach spaces. [ABSTRACT FROM AUTHOR]