Abstract
By principal motivation from the results of the new iterative scheme that produces faster results than K-iteration. In this article, we study generalized results by a new iteration scheme to approximate fixed points of generalized contraction and Suzuki non-expansive mappings. We establish strong convergence results of generalized contraction mappings of closed convex Banach space and also deduce data dependent results. Furthermore, we prove some weak and strong convergence theorems in the sense of generalized Suzuki non-expansive mapping by applying condition (C).
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