$H(\cdot,\cdot)$-mixed relaxed co-$\eta$-monotone mapping with an application for solving a resolvent equation problem

Abstract

In this paper, we define an $H(\cdot,\cdot)$-mixed relaxed co-$\eta$-monotone mapping and we apply the same for solving a resolvent equation problem in Hilbert spaces. We also prove some of the properties of $H(\cdot,\cdot)$-mixed relaxed co-$\eta$-monotone mapping. A mann-type iterative algorithm is developed to approximate the solution of resolvent equation problem. Convergence of the iterative sequences is also demonstrated.