Title: Equilibrium and mixed equilibrium problems on Hadamard manifolds

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.

DOI: 10.1504/IJMOR.2017.087742

International Journal of Mathematics in Operational Research, 2017 Vol.11 No.4, pp.480 - 496

Received: 18 Dec 2015
Accepted: 29 Mar 2016
Published online: 01 Nov 2017 *

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