M.R. Yadav, B.P. Tripathi
School of Studies in Mathematics
Pt.Ravishankar Shukla University
Raipur, Chhattisgarh, 492010, INDIA
Department of Mathematics
Govt. N.P.G. College of Science
Raipur, Chhattisgarh, 492001, INDIA

Abstract. In this paper, we consider a generalized iterative process and analyze a two-step iteration scheme for asymptotically nonexpansive mappings in uniformly convex Banach space. Our iteration scheme includes Ishikawa type and Mann type iterations as special cases. The results obtained in this paper represent an extension as well as refinement of previous known results. A new iterative scheme for approximating common fixed points of two asymptotically nonexpansive mapping is defined and we have proved weak and strong convergence theorems in a uniformly convex Banach space.

Received: June 7, 2012

AMS Subject Classification: 47H05, 47H10, 49M05

Key Words and Phrases: iteration process, asymptotically nonexpansive, condition (A'), L-Lipschitzian mapping, Opial's condition, common fixed point

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