Iterative algorithms for solutions of nonlinear equations in Banach spaces.

Doctoral Degree. University of KwaZulu-Natal, Durban.Abstract available in PDF

Alternative iterative methods for nonexpansive mappings, rates of convergence and application

Alternative iterative methods for a nonexpansive mapping in a Banach space are proposed and proved to be convergent to a common solution to a fixed point problem and a variational inequality. We give rates of asymptotic regularity for such iterations using proof-theoretic techniques. Some applications of the convergence results are presented

A general inexact iterative method for monotone operators, equilibrium problems and fıxed point problems of semigroups in Hilbert spaces

Let H be a real Hilbert space. Consider on H a nonexpansive family T = {T(t) :0 ≤ t < ∞} with a common fixed point, a contraction f with the coefficient

Alternative iterative methods for nonexpansive mappings, rates of convergence and applications

Alternative iterative methods for a nonexpansive mapping in a Banach space are proposed and proved to be convergent to a common solution to a fixed point problem and a variational inequality. We give rates of asymptotic regularity for such iterations using proof-theoretic techniques. Some applications of the convergence results are presented