Recurrent Inequalities and Some of their Applications to Picard and Mann Iterations

Abstract

Two lemmas concerning the superior bound of a numerical sequence satisfying a common recurrence inequality are given. As applications, the error estimations are obtained for the Picard and Mann iterations in the case of demicontractive mappings. Additional conditions that ensure the strong convergence in the same cases can be obtained on the basis of these lemmas.

Keywords

• recurrent inequalities
• fixed points
• iterative procedures