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

Abstract

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:

parallel to F(tau x boolean OR eta y) - tau F(x) boolean OR eta F(y)parallel to ˂= phi (tau x boolean OR eta y, tau X Lambda eta y),

where chi is a Banach lattice and phi : chi x chi -˃ chi is a mapping such that

phi(x,y) ˂= (tau eta)(alpha/2) phi (x/tau, y/eta)

for all tau, eta ˃= 1 and alpha is an element of [0,1/2).