R-linear and strong convergence of Tseng methods for solving certain split and non-split problems

Abstract

In the recent past, authors have fondly assumed the co-coercive condition for solving certain class of split inverse problems. Recently, some attempts have been made to relax this very strict condition, however, only few results exists in literature in such case. In this paper, we present some new Mann-type Tseng methods for solving split monotone variational inclusion and common fixed point problems for a finite collection of quasi-pseudocontractive operators. We prove strong convergence and R − linear convergence rate results of our methods, while the co-coerciveness property is dispensed with. Our methods incorporate the relaxation, inertial extrapolation and self-adaptive step size techniques to achieve better performance and faster convergence. With the aid of relevant numerical experiments, we showcase the performance profile of our methods in comparison with recent methods in literature.