A New Iterative Algorithm for Zeros of Generalized Phi-strongly Monotone and Bounded Maps with Application
C. E. Chidume *
African University of Science and Technology, Abuja, Nigeria
O. M. Romanus
African University of Science and Technology, Abuja, Nigeria
U. V. Nnyaba
African University of Science and Technology, Abuja, Nigeria
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Monotone mapping, generalized Φ -strongly monotone mappings, strong convergence