Split Variational Inclusion Problem and Fixed Point Problem for a Class of Multivalued Mappings in <i>CAT</i>(0) Spaces

Abstract

The aim of this paper is to introduce a modified viscosity iterative method to approximate a solution of the split variational inclusion problem and fixed point problem for a uniformly continuous multivalued total asymptotically strictly pseudocontractive mapping in C A T ( 0 ) spaces. A strong convergence theorem for the above problem is established and several important known results are deduced as corollaries to it. Furthermore, we solve a split Hammerstein integral inclusion problem and fixed point problem as an application to validate our result. It seems that our main result in the split variational inclusion problem is new in the setting of C A T ( 0 ) spaces.

Keywords

• split variational inclusion problem
• fixed point problem
• <i>CAT</i>(0) space
• total asymptotically strictly pseudocontractive mapping