Approximation of Solutions of Inclusion Problems with Applications to Hammerstein Equation and Image Restoration

Abstract

Monotone operators and accretive operators are essential to modern optimization and xed point theory. Monotone operators were rst discovered by Minty in real Hilbert spaces to aid in the abstract study of electrical networks. Interest in the study of monotone operators stems mainly from their rm connection with optimization problems. Accretive operators were introduced independently by Browder and Kato. Interest in the study of accretive operators stems mainly form their rm connection with the existence theory for nonlinear evolution equations in Banach spaces. This thesis provides an in-depth study of iterative methods for approximating solutions of nonlinear equations involving monotone and accretive operators in Banach spaces more general than Hilbert spaces. Our objectives are: to develop new theorems and iterative algorithms; apply these theorems to problems such as, Hammerstein equation, convex minimization problems, image restoration problems and, finally, conduct numerical experiments to show the efficiency of our algorithms.