Abstract
In this paper, we suggest and analyze an iterative method for solving the equilibrium problems on Hadamard manifolds using the auxiliary principle technique. We also consider the convergence analysis of the proposed method under suitable conditions. Some special cases are considered. Results and ideas of this paper may stimulate further research in this fascinating and interesting field.MSC:49J40, 90C33, 26D10, 39B62.
Highlights
1 Introduction Equilibrium problems theory provides us with a unified, natural, novel and general framework to study a wide class of problems, which arise in finance, economics, network analysis, transportation and optimization
Nemeth [ ], Tang et al [ ], Noor et al [, ] and Colao et al [ ] have considered the variational inequalities and equilibrium problems on Hadamard manifolds. They have studied the existence of solutions of equilibrium problems under some suitable conditions
Our result includes the recent results of Tang et al [ ] for variational inequalities on a Hadamard manifold
Summary
Equilibrium problems theory provides us with a unified, natural, novel and general framework to study a wide class of problems, which arise in finance, economics, network analysis, transportation and optimization. This theory has applications across all disciplines of pure and applied sciences. Much attention has been given to study the variational inequalities, equilibrium and related optimization problems on the Riemannian manifold and Hadamard manifold. This framework is useful for the development of various fields. We hope that the technique and idea of this paper may stimulate further research in this area
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