Krasnoselski-Mann type iterative method for hierarchical fixed point problem and split mixed equilibrium problem |
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Authors: | K R Kazmi Rehan Ali Mohd Furkan |
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Institution: | 1.Department of Mathematics,Aligarh Muslim University,Aligarh,India |
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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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