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Strong Convergence Theorems for Variational Inequalities and Fixed Point Problems of Asymptotically Strict Pseudocontractive Mappings in the Intermediate Sense

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Abstract

The purpose of this paper is to investigate the problem of finding a common element of the set of fixed points of an asymptotically strict pseudocontractive mapping in the intermediate sense and the set of solutions of the variational inequality problem for a monotone, Lipschitz continuous mapping. We introduce a modified hybrid Mann iterative scheme with perturbed mapping which is based on well-known CQ method, Mann iteration method and hybrid (or outer approximation) method. We establish a strong convergence theorem for three sequences generated by this modified hybrid Mann iterative scheme with perturbed mapping. Utilizing this theorem, we also design an iterative process for finding a common fixed point of two mappings, one of which is an asymptotically strict pseudocontractive mapping in the intermediate sense and the other taken from the more general class of Lipschitz pseudocontractive mappings.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China

    Lu-Chuan Ceng

  2. Scientific Computing Key Laboratory of Shanghai Universities, Shanghai, 200234, China

    Lu-Chuan Ceng

  3. Center for General Education, Kaohsiung Medical University, Kaohsiung, 807, Taiwan

    Jen-Chih Yao

Authors
  1. Lu-Chuan Ceng
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  2. Jen-Chih Yao
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Correspondence to Jen-Chih Yao.

Additional information

This research was partially supported by the National Science Foundation of China (11071169), Innovation Program of Shanghai Municipal Education Commission (09ZZ133), Leading Academic Discipline Project of Shanghai Normal University (DZL707), Science and Technology Commission of Shanghai Municipality Grant (075105118), and Shanghai Leading Academic Discipline Project (S30405).

This research was partially supported by the Grant NSC 99-2221-E-110-038-MY3.

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Ceng, LC., Yao, JC. Strong Convergence Theorems for Variational Inequalities and Fixed Point Problems of Asymptotically Strict Pseudocontractive Mappings in the Intermediate Sense. Acta Appl Math 115, 167–191 (2011). https://doi.org/10.1007/s10440-011-9614-x

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