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Iterative Approximations of Fixed Points for Non-Lipschitzian Asymptotically Pseudocontractive Mappings

Ming Yao Xiong

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Abstract

The purpose of this paper is to investigate the strong convergence problem of the modified Ishikawa and Mann iterative processes with errors for approximating fixed points of non-Lipschitzian asymptotically pseudocontractive mappings in an arbitrary real Banach space.Under the condition of removing the restriction‖Tnxn-xn‖→0(n→∞)and {xn} is bounded,it is proven that the relevant results remain true.The results presented in this paper improve and extend some recent existing results.

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What this paper is about

The purpose of this paper is to investigate the strong convergence problem of the modified Ishikawa and Mann iterative processes with errors for approximating fixed points of non-Lipschitzian asymptotically pseudocontractive mappings in an arbitrary real Banach space.Under the condition of removing the restriction‖Tnxn-xn‖→0(n→∞)and {xn} is bounded,it is proven that the relevant results remain true.The results presented in this paper improve and extend some recent existing results.

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Available abstract

The purpose of this paper is to investigate the strong convergence problem of the modified Ishikawa and Mann iterative processes with errors for approximating fixed points of non-Lipschitzian asymptotically pseudocontractive mappings in an arbitrary real Banach space.Under the condition of removing the restriction‖Tnxn-xn‖→0(n→∞)and {xn} is bounded,it is proven that the relevant results remain true.The results presented in this paper improve and extend some recent existing results.

Key concepts: Banach space, Fixed point, Convergence (economics), Mathematics, Bounded function, Applied mathematics, Iterative method, Discrete mathematics

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