LAUSR

Let E be a uniformly convex and uniformly smooth real Banach space with dual space $$E^*$$E∗ and C be a nonempty, closed and convex subset of E. Let $$A:E\rightarrow E^*$$A:E→E∗ be a generalized $$\Phi $$Φ-strongly monotone and bounded map and let $$T_i:C\rightarrow E, i=1,2,3,\ldots , N$$Ti:C→E,i=1,2,3,…,N be a finite family of quasi-$$\phi $$ϕ-nonexpansive maps such that $$\cap _{i=1}^{N} F(T_{i})\ne \emptyset $$∩i=1NF(Ti)≠∅. Suppose $$VI(A,\cap _{i=1}^{N} F(T_{i}))\ne \emptyset $$VI(A,∩i=1NF(Ti))≠∅. A new iterative algorithm that converges strongly to a point in $$VI(A,\cap _{i=1}^{N} F(T_{i}))$$VI(A,∩i=1NF(Ti)) is constructed. Results obtained are applied to a convex optimization problem. Furthermore, the theorems proved complement, improve and unify several recent important results. Finally, we consider a family $$\{T_i\}_{i=1}^N$${Ti}i=1N of maps where for each $$i,\, T_i $$i,Ti maps E into its dual space $$E^*$$E∗ and prove a strong convergence theorem for $$VI(A, \cap _{i=1}^{N} F(T_{i}))$$VI(A,∩i=1NF(Ti)), where $$F_J(T_i)$$FJ(Ti) is the set of J-fixed points introduced by Chidume and Idu.