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arXiv · 2112.09901

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

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

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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Markjoe O. Uba, Maria A. Onyido, Cyril I. Udeani, Peter U. Nwokoro. 2021-12-18. 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. https://arxiv.org/abs/2112.09901

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