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In this paper, we solve the additive ρ-functional equations f(x + y) - f(x) - f(y) = ρ(2f(x + y/2)-f(x)-f(y)), (0.1) 2f(x + y) - f(x) - f(y) = ρ (f(x + y) - f(x) - f(y)) ; (0.2) where ρ is a fixed non-Archimedean number or a fixed real or complex number with ρ≠1. Using the direct method, we prove the Hyers-Ulam stability of the additive ρ- functional equations (0.1) and (0.2) in non-Archimedean Banach spaces and in Ba- nach spaces. [ABSTRACT FROM AUTHOR]

In this paper, we solve the following additive p-functional inequalities N(f(x + y) - f(x) - f(y), t) ⩽ N (P ( 2f ( x + y / 2 ) - f(x) - f(y) ), t ) (0.1) and N ( 2f ( x + y / 2 ) - f(x) - f(y), t ) ⩽ N(p (f(x + y) - f(x) - f(y)) , t) (0.2) in fuzzy normed spaces, where p is a fixed real number with ∣p∣ < 1. Using the fixed point method, we prove the Hyers-Ulam stability of the additive p-functional inequalities (0.1) and (0.2) in fuzzy Banach spaces. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to study the periodic character and the global stability of the positive solutions of the difference equation xn+1 = axn + bxn-k + cxn-l - dxn-s/exn-s - αxn-t, n = 0, 1, ..., where the parameters a, b, c, d, e and α are positive real numbers and the initial conditions x-σ, x-σ+1, ..., x-1, x0 are positive real numbers where σ = max{s, t, k,}. Some numerical examples were given to illustrate our results. [ABSTRACT FROM AUTHOR]