An hierarchical circularly iterative method is introduced for solving a system of variational circularly inequalities with set of fixed points of strongly quasi-nonexpansive mapping problems in this paper. Under some suitable conditions, strong convergence results for the hierarchical circularly iterative sequence are proved in the setting of Hilbert spaces. Our scheme can be regarded as a more general variant of the algorithm proposed by Maingé.
We introduce a k-strictly pseudononspreading
multivalued in Hilbert spaces more general than the class of nonspreading
multivalued. We establish some weak convergence theorems of the sequences
generated by our iterative process. Some new iterative sequences for finding a
common element of the set of solutions for equilibrium problem was introduced.
The results improve and extend the corresponding results of Osilike Isiogugu  (Nonlinear Anal.74 (2011)) and others.
this paper, we introduce a new hybrid iterative algorithm for finding a common
element of the set of common fixed points of a finite family of uniformly
asymptotically nonexpansive semigroups and the set of solutions of an
equilibrium problem in the framework of Hilbert spaces. We then prove the strong
convergence theorem with respect to the proposed iterative algorithm. Our
results in this paper extend and improve some recent known results.