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2013•Fixed Point Theory and ApplicationsOpen access

Strong convergence to a fixed point of a total asymptotically nonexpansive mapping

Gang Eun Kim

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Abstract

In this paper, we prove strong convergence for the modified Ishikawa iteration process of a total asymptotically nonexpansive mapping satisfying condition ( A ) in a real uniformly convex Banach space. Our result generalizes the results due to Rhoades (J. Math. Anal. Appl. 183:118-120, 1994). MSC: 47H05, 47H10.

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In this paper, we prove strong convergence for the modified Ishikawa iteration process of a total asymptotically nonexpansive mapping satisfying condition ( A ) in a real uniformly convex Banach space. Our result generalizes the results due to Rhoades (J. Math. Anal. Appl. 183:118-120, 1994). MSC: 47H05, 47H10.

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Available abstract

In this paper, we prove strong convergence for the modified Ishikawa iteration process of a total asymptotically nonexpansive mapping satisfying condition ( A ) in a real uniformly convex Banach space. Our result generalizes the results due to Rhoades (J. Math. Anal. Appl. 183:118-120, 1994). MSC: 47H05, 47H10.

Key concepts: Fixed point, Banach space, Mathematics, Differential geometry, Regular polygon, Convergence (economics), Pure mathematics, Discrete mathematics

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