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A modified iterative method for capturing a common solution of split generalized equilibrium problem and fixed point problem. (English) Zbl 1423.47045

Summary: A new iterative method is proposed based on hybrid viscosity approximation method and hybrid steepest-descent method to approximate a common solution of a split generalized equilibrium problem and a fixed point problem of a finite collection of nonexpansive mappings. We prove that the sequences generated by the iterative scheme converges strongly to a common solution of the above problems. Applications and numerical results are also given to illustrate the effectiveness and superiority of the proposed algorithm.

MSC:

47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
49J40 Variational inequalities
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