A hybrid scheme for fixed points of a countable family of generalized nonexpansive-type maps and finite families of variational inequality and equilibrium problems, with applications

Uba, Markjoe O., Onyido, Maria A., Udeani, Cyril I. and  Nwokoro, Peter U.

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Let C be a nonempty closed and convex subset of a uniformly smooth and uniformly convex real Banach space E  with dual space E^*. We present a novel hybrid method for finding a common solution of a family of equilibrium problems, a common solution of a family of variational inequality problems and a common element of fixed points of a family of a general class of nonlinear nonexpansive maps. The sequence of this new method is proved to converge strongly to a common element of the families. Our theorem and its applications complement, generalize, and extend various results in literature.


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Nwokoro, Peter U., Onyido, Maria A., Uba, Markjoe O., Udeani, Cyril I.