Convergence Analysis for Variational Inclusion Problems Equilibrium Problems and Fixed Point in Hadamard Manifolds

Abstract

The purpose of this paper is to introduce a new splitting iterative algorithm for finding a common solution of a system of quasi-variational inclusion problems, equilibrium problems and fixed point for quasi-nonexpansive mappings in Hadamard manifolds. It is shown that under mild conditions, the iterative sequence generated by the proposed algorithm converges to a common solution. As applications, we apply our results to study the minimization problems and saddle point problems in Hadamard manifolds.

Keywords:

• Equilibrium problem
• Hadamard manifold
• maximal monotone vector field
• quasi-nonexpansive mappings
• quasi-variational inclusion problem

Subjclass (2010):

• 26B25
• 47H05
• 47J25
• 58A05
• 58C30
• 90C33

Additional information

Funding

This work was supported by the Natural Science Foundation of China Medical University, Taiwan, and by the Natural Science Foundation of Kaohsiung Medical University Hospital.