Mann Iteration Process for Monotone Nonexpansive Mappings with a Graph

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Let (X,.) be a Banach space. Let C be a nonempty, bounded, closed, and convex subset of X and T: C → C be a G-monotone nonexpansive mapping. In this work, it is shown that the Mann iteration sequence defined by xₙ₊₁ = tₙ T(xₙ) + (1-tₙ)xₙ, n = 1, 2, can be proved the existence of a fixed point of G-monotone nonexpansive mappings.