Authors: Shreyasi Jana; Chandal Nahak
Addresses: Department of Mathematics, IIT Kharagpur, Kharagpur 721302, India ' Department of Mathematics, IIT Kharagpur, Kharagpur 721302, India
Abstract: In this paper, we study equilibrium problems and mixed equilibrium problems on Hadamard manifolds. Using the KKM technique, we establish the existence of solutions of the stated problems under the generalised monotonicity assumptions on the functions involved. We construct some examples to justify our work in Hadamard manifold. We also investigate the proximal point algorithm to solve mixed equilibrium problems on Hadamard manifolds. Our results and ideas may stimulate further research in this fascinating and interesting field of nonlinear space.
Keywords: Hadamard manifold; equilibrium problems; pseudomonotonicity; KKM mappings.
International Journal of Mathematics in Operational Research, 2017 Vol.11 No.4, pp.480 - 496
Available online: 26 Oct 2017 *Full-text access for editors Access for subscribers Purchase this article Comment on this article