Abstract
The aim of this work is twofold; first, to give an extension to split mixed equilibrium problem. Secondly, we suggest and analyze an iterative method based on Mann iterative method and Halpern iterative method to find a common solution of split mixed equilibrium problem and fixed point problem for a nonexpansive mapping in the framework of real Hilbert spaces. Further, under some mild conditions, strong convergence theorem is obtained by the sequences generated by the proposed iterative method, which solves the variational inequality problem. Furthermore, we derived some consequences from our main result and provide some numerical experiments. Our results can be viewed as significant extension and generalization of the previously known results for solving equilibrium problems.
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