Convergence theorems for strongly pseudocontractive operators

Priya Raphael

Abstract


In this paper, the convergence of Ishikawa type iteration process to the unique fixed point of a strongly pseudocontractive operator in real Banach space is established. The convergence of a Mann type iteration scheme to a fixed point of a continuous strongly pseudocontractive operator with specific pseudocontractive parameter in Hilbert space is also proved.

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References


R. P. Agarwal, D. ORegan and D. R. Sahu, Fixed point theory for

Lipschitzian-type mappings with applications, Springer, New York, 2009.

S. S. Chang, Y. J. Cho, B. S. Lee, J. S. Jung and S. M. Kang, Iterative approximations of fixed points and solutions for strongly accretive

and strongly pseudocontractive mappings in Banach spaces, J. Math. Anal. Appl. 224 (1998), 149-165.

C. E. Chidume, Approximation of fixed points of strongly pseudo-contractive mappings, Proc. Amer. Math. Soc. 120 (1994), 545-551.

C. E. Chidume and M. O. Osilike, Ishikawa iteration process for nonlinear Lipschitz strongly accretive mappings, J. Math. Anal. Appl. 192 (1995), 727-741.

L. J. Ciric and J. S. Ume, Ishikawa iterative process for strongly pseudocontractive operators in arbitrary Banach spaces, Math. Commun. 8 (2003), 43-48.

L. Deng, An iterative process for nonlinear Lipschitzian and strongly

accretive mappings in uniformly convex and uniformly smooth Banach spaces, Acta Appl. Math. 32 (1993), 183-196.

S. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc. 44 (1974), 147-150.

W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc.

(1953), 506-510.

C. H. Morales, J. S. Jung, Convergence of paths for pseudocontractive

mappings in Banach spaces, Proc. Amer. Math. Soc. 120 (11) (2000),

-3419.

M. O. Osilke, A note on the stability of iteration procedures for strongly pseudocontractions and strongly accretive type equations, J. Math. Anal. Appl. 250 (2000), 726-730.

A. Ra q, Implicit fixed point iterations, Rostock. Math. Kolloq. 62

(2007), 21-39.

S. M. Soltuz, A correction for a result on convergence of Ishikawa iteration for strongly pseudocontractive maps, Math. Commun. 7 (2002), 61-64.

Y. G. Xu, Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive operator equations, J. Math. Anal. Appl. 224 (1998), 91-101.

H. Y. Zhou and Y. Jia, Approximation of fixed points of strongly

pseudocontractive maps without Lipschitz assumption, Proc. Amer. Math. Soc. 125 (1997), 1705-1709.

H. Y. Zhou, Stable iteration procedures for strong pseudocontractions

and nonlinear equations involving accretive operators without Lipschitz assumption, J. Math. Anal. Appl. 230 (1999), 1-10.


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