Convergence of a One-step Iteration Scheme for Quasi-asymptotically Nonexpansive Mappings

In this paper, we use a one-step iteration scheme to approximate common fixed points of two quasi-asymptotically nonexpansive mappings. We prove weak and strong convergence theorems in a uniformly convex Banach space. Our results generalize the corresponding results of Yao and Chen [15] to a wider class of mappings while extend those of Khan, Abbas and Khan [4] to an improved one-step iteration scheme without any condition and improve upon many others in the literature.

• Safeer Hussain Khan

• One-step iteration scheme
• asymptotically quasi non expansive mapping
• common fixed point
• condition (a')
• weak and strong convergence.

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