A New Iterative Algorithm for Zeros of Generalized Phi-strongly Monotone and Bounded Maps with Application

Let E be a uniformly smooth and uniformly convex real Banach space and A : E → E* be a generalized Φ-strongly monotone and bounded map with A-1(0) ≠ θ. A new iterative process is constructed and proved to converge strongly to the unique solution of the equation Au = 0. An application to convex minimization problem is given. Furthermore, the technique of proof is of independent interest.