Banach space,the necessary and sufficient condition for the convergence of implicit iteration process for strictly pseudocontractive maps is the space satisfy the opial condition.

In this paper,the criteria of uniform opial condition are given in orlicz sequence space equipped with luxemburg norm and orlicz norm.

A generalized Opail coneiticn is used to prove two coupled fixed point theorems for compressed mappings and to obtain the existence of approximate coupled and fixed point theorem for a class of nonexpansive mappings in the breadth space with generalized Opial condition and finally the conclusion is generalized into weak and tight convex.

Let X be a Banach space, (X,τ) a local convex linear topological space, C a τ-sequence compact convex subset of X, and T an asymptotically nonexpansive mapping with the property (Γ) from C to itself, we give the ergodic convergence theorem for asymptotically nonexpansive mapping under uniformly τ-opial condition.