STABILITY OF A LATTICE PRESERVING FUNCTIONAL EQUATION ON RIESZ SPACE: FIXED POINT ALTERNATIVE.

The aim of this paper is to investigate Hyers-Ulam stability of the following lattice preserving functional equation on Riesz space with fixed point method: ||F(τx V ηy) -- τF(x) V ηF(y)|| ≤ φ(τx V ηy, τx Λ ηy), where X is a Banach lattice and φ : X × X ↑ X is a mapping such that φ(x,y)≤(τη)α/2 φ(x/τ,y/η) for all τ,η ≥ 1 and α ∈[0,1/2). [ABSTRACT FROM AUTHOR]