A new efficient algorithm for finding common fixed points of multivalued demicontractive mappings and solutions of split generalized equilibrium problems in Hilbert spaces

The purpose of this article is to present a new iterative technique for approximating solutions of split generalized equilibrium problem and common fixed points of multivalued demicontractive mappings satisfying the gate conditions in real Hilbert spaces. Unlike the earlier results in this direction, we obtain a strong convergence result using an Armijo line search rule for determining the best appropriate step size for the next iteration. Also, our algorithm is designed in such a way that it does not require a projection onto the feasible set. We further give an analysis of the convergence rate of our method which is shown to be (Formula presented.). Finally, the performances and comparisons with some existing methods are presented through numerical experiments. This result extends, generalizes and improves many of the existing related results in a unified way.