Ishikawa iterative process for hemicontractive multi-valued non-self mappings in CAT(0) spaces

Abstract

Our purpose in this paper is to construct Ishikawa iterative scheme formulti-valued non-self mappings in CAT(0) spaces. Then we obtain strong convergence of the scheme to a fixed point of multi-valued hemicontractive non-self mapping in a complete CAT(0) space. In addition, we define pseudocontractive mapping in CAT(0) spaces and show that a pseudocontractive mapping T with \(F(T)\not =\emptyset \) and \(Tp=\{p\}, \forall p\in F(T)\) is hemicontractive mapping. Furthermore, we give an example of hemicontractive mapping which is not pseudocontarctive to show that the converse is not necessarily true. Our theorems improve and unify most of the results in the literature.