Convergence of Iterative Algorithms for Continuous Pseudocontractive Mappings

Jong Soo Jung

In this paper, we prove strong convergence of a path for a convex combination of a pseudocontractive type of operators in a real reflexive Banach space having a weakly continuous duality mapping $J_\varphi$ with gauge function $\varphi$. Using path convergency, we establish strong convergence of an implicit iterative algorithm for a pseudocontractive mapping combined with a strongly pseudocontractive mapping in the same Banach space.