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.

 

Additional Information

Author(s)

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

DOI

https://doi.org/10.37193/CJM.2023.01.19