Fixed Points of Contractive-Like Operators by a Faster Iterative Process
Commenced in January 2007
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Fixed Points of Contractive-Like Operators by a Faster Iterative Process

Authors: Safeer Hussain Khan

Abstract:

In this paper, we prove a strong convergence result using a recently introduced iterative process with contractive-like operators. This improves andgeneralizes corresponding results in the literature in two ways: iterativeprocess is faster, operators are more general. At the end, we indicatethat the results can also be proved with the iterative process witherror terms.

Keywords: Contractive-like operator, iterative process, fixed point, strong convergence.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1336326

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References:


[1] V. Berinde, A convergence theorem for some mean value fixed point iterations procedures, Dem. Math., 38(1)2005, 177-184.
[2] S.K. Chatterjea, Fixed point theorems, C.R. Acad. Bulgare Sci., 25 (1972), 727-730.
[3] 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.
[4] C.O. Imoru, M.O. Olatinwo, On the stability of Picard and Mann iteration processes, Carpathian Journal of Mathematics, 19, 155-160 (2003).
[5] S. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc., 44 (1974), 147-150.
[6] L. S. Liu, Ishikawa and Mann Iteration process with errors for nonlinear strongly accretive mappings in Banach spaces, J. Math. Anal. Appl. 194(1) (1995), 114-125.
[7] R. Kannan, Some results on fixed points,Bull. Calcutta Math. Soc., 10(1968), 71-76.
[8] S.H. Khan, A Picard-Mann hybrid iterative process, Fixed Point Theory and Applications 2013, 2013:69.
[9] S.H. Khan, Approximating Common fixed points by an iterative process involving two steps and three mappings, Journal of Concrete and Applicable Mathematics, Vol 8, number 3, 407-415, 2010.
[10] S.H. Khan, Fixed points of quasi-contractive type operators in normed spaces by a three-step iteration process, Proceedings of the World Congress on Engineering 2011 Vol I, WCE 2011, July 6 - 8, 2011, London, U.K, pp 144-147.
[11] W.R. Mann, Mean value methods in iterations, Proc. Amer. Math. Soc., 4 (1953), 506-510.
[12] E. Picard, Memoire sur la theorie des equations aux deriveespartielles et la methode des approximations successives, J. Math. Pures et Appl.,6, 145-210 (1890).
[13] Y. Xu, Ishikawa and Mann Iteration process with errors for nonlinear strongly accretive operator equations, J. Math. Anal. Appl. 224 (1998), 91-101.
[14] T. Zamfirescu, Fix point theorems in metric spaces, Arch. Math. (Basel), 23(1972), 292-298.