An iterative algorithm for a general system of variational inequalities and fixed point problems in q‐uniformly smooth Banach spaces

In this paper, we introduce a new iterative algorithm for finding a common element of the set of common fixed points of an infinite family of notself strict pseudocontractions and the set of solutions of a general variational inequality problem for finite inverse‐strongly accretive mappings in q‐uniformly smooth Banach space. We obtain some strong convergence theorems under suitable conditions. Our results improve and extend the recent results announced by Qin et al. (2009), Yao et al. (2010) and many others.