ON A GENERAL CLASS OF MULTI-VALUED STRICTLY PSEUDOCONTRACTIVE MAPPINGS - Chidume, C.E.; Okpala, M.E. (Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO), 2014)
In this paper, a general class of multi-valued strictly pseudocontractive mappings, which properly includes the class of multi-valued k-strictly pseudocontractive mappings, is introduced. Furthermore, it is proved that if T belongs to this class of mappings and the set of fixed points of T is nonempty, a Krasnoselskii-type sequence is constructed and proved to be an approximate fixed point sequence of T. Finally, convergence of the sequence to a fixed point of T is proved under appropriate additional conditions.