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Viscosity iterative process for demicontractive mappings and multivalued mappings and equilibrium problems

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Abstract

In this paper, we introduce a general iterative scheme based on the viscosity approximation method for finding a common element of the set of solutions of the equilibrium problem and the set of all fixed points of a demicontractive mapping and a generalized nonexpansive multivalued mapping. Then, we prove the strong convergence of the iterative scheme to find a unique solution of the variational inequality which is the optimality condition for the minimization problem. The main results presented in this paper extend various results existing in the current literature.

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Authors and Affiliations

  1. Department of Mathematics, University of Science and Technology of Mazandaran, Behshahr, Iran

    M. Eslamian

  2. Department of Applied Mathematics, Iran University of Science and Technology, Tehran, Iran

    R. Saadati & J. Vahidi

Authors
  1. M. Eslamian
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  2. R. Saadati
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  3. J. Vahidi
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Correspondence to M. Eslamian.

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Communicated by Carlos Conca.

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Eslamian, M., Saadati, R. & Vahidi, J. Viscosity iterative process for demicontractive mappings and multivalued mappings and equilibrium problems. Comp. Appl. Math. 36, 1239–1253 (2017). https://doi.org/10.1007/s40314-015-0292-6

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  • DOI: https://doi.org/10.1007/s40314-015-0292-6

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