In this paper, we study synchronal and cyclic algorithms for finding a common fixed point of a finite family of strictly pseudocontractive mappings, which solve the variational inequality where f is a contraction mapping, G is an η-strongly accretive and L-Lipschitzian operator, is a positive integer, are arbitrary fixed constants, and are N-strict pseudocontractions. Furthermore, we prove strong convergence theorems of such iterative algorithms in a real q-uniformly smooth Banach space. The results presented extend, generalize and improve the corresponding results recently announced by many authors. MSC:47H06, 47H09, 47H10, 47J05, 47J20, 47J25.