CONVERGENCE IN NORM OF MODIFIED KRASNOSELSKII-MANN ITERATION FOR FIXED POINTS OF ASYMPTOTICALLY DEMICONTRACTIVE MAPPINGS

CONVERGENCE IN NORM OF MODIFIED KRASNOSELSKII-MANN ITERATION FOR FIXED POINTS OF ASYMPTOTICALLY DEMICONTRACTIVE MAPPINGS

ABSTRACT

This project report deals with the class of asymptotically demicontractive nmappings in Hilbert spaces. We noted some historical aspects concerning the concept of asymptotically demicontractivity and studied a regularized variant of the Krasnoselskii-Mann iteration scheme, which ensured the strong convergence of the generated sequence towards the least norm element of the set of fixed points of asymptotically demicontractive mapping.