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Krasnoselski-Mann type iterative method for hierarchical fixed point problem and split mixed equilibrium problem

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Abstract

In this paper, we suggest and analyze a Krasnoselski-Mann type iterative method to approximate a common element of solution sets of a hierarchical fixed point problem for nonexpansive mappings and a split mixed equilibrium problem. We prove that sequences generated by the proposed iterative method converge weakly to a common element of solution sets of these problems. Further, we derive some consequences from our main result. Furthermore, we extend the considered iterative method to a split monotone variational inclusion problem and deduce some consequences. Finally, we give a numerical example to justify the main result. The method and results presented in this paper generalize and unify the corresponding known results in this area.

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Authors and Affiliations

  1. Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India

    K. R. Kazmi, Rehan Ali & Mohd Furkan

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  1. K. R. Kazmi
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  2. Rehan Ali
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  3. Mohd Furkan
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Correspondence to K. R. Kazmi.

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Kazmi, K.R., Ali, R. & Furkan, M. Krasnoselski-Mann type iterative method for hierarchical fixed point problem and split mixed equilibrium problem. Numer Algor 77, 289–308 (2018). https://doi.org/10.1007/s11075-017-0316-y

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  • DOI: https://doi.org/10.1007/s11075-017-0316-y

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