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Analele Universitatii "Ovidius" Constanta - Seria Matematica

The Journal of "Ovidius" University of Constanta

Editor-in-Chief: Flaut, Cristina

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ISSN
1844-0835
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An iteration process for common fixed points of two nonself asymptotically nonexpansive mappings

Sezgin Akbulut
Published Online: 2013-05-17 | DOI: https://doi.org/10.2478/v10309-012-0002-y

Abstract

In this paper, we introduce an iteration process for approximating common fixed points of two nonself asymptotically nonexpansive map- pings in Banach spaces. Our process contains Mann iteration process and some other processes for nonself mappings but is independent of Ishikawa iteration process. We prove some weak and strong convergence theorems for this iteration process. Our results generalize and improve some results in contemporary literature.

Keywords: Iteration Process; Nonself Asymptotically Nonexpansive Mapping; Common Fixed Point; Condition (A′); Weak and Strong Convergence

  • [1] R.P.Agarwal, Donal O’Regan and D.R. Sahu, Iterative construction of fixed points of nearly asymptotically nonexpansive mappings, J. Nonliear Convex. Anal.8(1)(2007), 61-79.Google Scholar

  • [2] C.Chidume, E. U.Ofoedu, H.Zegeye, Strong and weak convergence theorems for asymptotically nonexpansive mappings, J. Math. Anal.Appl. 280 (2003), 364-374.Google Scholar

  • [3] G. Das and J. P. Debata, Fixed points of Quasi-nonexpansive mappings, Indian J. Pure. Appl. Math., 17 (1986), 1263-1269.Google Scholar

  • [4] J.G.Falset, W.Kaczor, T.Kuzumow, S.Reich, Weak convergence theorems for asymptotically nonexpansive mappings and semigroups, Nonlinear Anal.,TMA 43 (2001), 377-401.Google Scholar

  • [5] H. Fukhar-ud-din and S. H. Khan, Convergence of iterates with errors of asymptotically quasi-nonexpansive mappings and applications, J. Math. Anal. Appl. 328 (2007), 821-829.Google Scholar

  • [6] K. Goebel and W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 35(1) (1972), 171-174.CrossrefGoogle Scholar

  • [7] W.Kaczor, Weak convergenceof almost orbits of asymptotically nonexpansive semigroups, J. Math. Anal. Appl. 272 (2002), 565-574.Google Scholar

  • [8] S. H. Khan and W. Takahashi, Approximating common fixed points of two asymptotically nonexpansive mappings, Sci. Math. Jpn., 53(1) (2001), 143-148.Google Scholar

  • [9] Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc., 73 (1967), 591-597.Google Scholar

  • [10] J. Schu, Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bull. Austral. Math. Soc. 43 (1991), 153-159.Google Scholar

  • [11] W. Takahashi, Iterative methods for approximation of fixed points and their applications, J.Oper.Res.Soc. Jpn., 43(1) (2000), 87 -108.CrossrefGoogle Scholar

  • [12] W. Takahashi and T. Tamura, Limit theorems of operators by convex combinations of nonexpansive retractions in Banach spaces, J.Approx.Theory, 91(3) (1997), 386 -397.CrossrefGoogle Scholar

  • [13] L. Wang, Strong and weak convergence theorems for common fixed points of nonself asymptotically nonexpansive mappings, J. Math. Anal. Appl. 323 (2006) 550-557.Google Scholar

  • [14] S. Thianwan, Common fixed point of new iterations for two asymptotically nonexpansive nonself-mappings in a Banach space, J. Comput. Appl. Math. 224 (2009) 688-695.Google Scholar

  • [15] H. Zhou, R.P. Agarwal, Y.J.Cho, Y.S.Kim, Nonexpansive mappings and iterative methods in uniformly convex Banach spaces, Georgian Mathematical Journal, 9 (2002), No.3, 591-600. Google Scholar

About the article

Published Online: 2013-05-17

Published in Print: 2012-05-01


Citation Information: Analele Universitatii "Ovidius" Constanta - Seria Matematica, ISSN (Online) 1844-0835, DOI: https://doi.org/10.2478/v10309-012-0002-y.

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