Existence and convergence theorems of fixed points for multi-valued SCC-, SKC-, KSC-, SCS- and C-type mappings in hyperbolic spaces
Shih-sen Chang, Ravi P. Agarwal, Lin Wang · Fixed Point Theory and Applications · 2015
Abstract The purpose of this paper is to introduce the concepts of multi-valued SCC-, SKC-, KSC-, SCS- and C-type mappings and propose a classical Kuhfitting-type iteration (Kuhfitting in Pac. J. Math. 97(1):137-139, 1981) for finding a common fixed point of the SKC-, KSC-, SCS- and C-type multi-valued mappings in the setting of hyperbolic spaces. Under suitable conditions some Δ-convergence theorems and strong convergence theorems for the iterative sequence generated by the proposed scheme to approximate a common fixed point of a finite family of SKC-, KSC-, SCS- and C-type multi-valued mappings are proved. The results presented in the paper extend and improve some recent results announced in the current literature.