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Jong Kyu Kim
Prof. Jong Kyu Kim
Kyungnam University, Republic of Korea
On the Bruck’s Ergodic Iteration Method for Solving the Ky Fan Inequalities

We introduce a new iteration algorithm for solving the Ky Fan inequality over the fixed point set of a nonexpansive mapping, where the cost bifunction is monotone without Lipschitz-type continuity. The algorithm is based on the idea of the ergodic iteration method for solving multi-valued variational inequality which is proposed by Bruck and the auxiliary problem principle for equilibrium problems. By choosing suitable regularization parameters, we also present the convergence analysis in detail for the algorithm and give some illustrative examples. 

Keyword: Ky Fan inequalities, monotonicity, fixed points, nonexpansive mappings. 

Jong Kyu Kim received the Ph.D. degree in Mathematics from the Busan National University, Korea in 1988. Now he is a full Professor at Department of Mathematics Education in Kyungnam University. He is the Chief-Editor of the journals ‘Nonlinear Functional Analysis and Applications(NFAA)’, ‘International Journal of Mathematical Sciences(IJMS)’ and ‘East Asian Mathematical Journal(EAMJ)’. He is an associate editor for many international mathematical journals. He has also delivered invited talks in many international conferences held in European, American and Asian countries. He has also organized many times international Conference, for example “Nonlinear Functional Analysis and Applications(NFAA)” His current research interests include optimization, nonlinear functional analysis, variational inequality problems, equilibrium problems, operator equations and fixed point problems. He has published over 320 research papers in the journals of international repute.
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