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http://dx.doi.org/10.11568/kjm.2016.24.1.51

REGULARIZED EQUILIBRIUM PROBLEMS IN BANACH SPACES  

Salahuddin, Salahuddin (Department of Mathematics Jazan University)
Publication Information
Korean Journal of Mathematics / v.24, no.1, 2016 , pp. 51-63 More about this Journal
Abstract
In this works, we consider a class of regularized equilibrium problems in Banach spaces. By using the auxiliary principle techniques to suggest some iterative schemes for regularized equilibrium problems and proved the convergence of these iterative methods required either pseudoaccretivity or partially relaxed strongly accretivity.
Keywords
Regularized equilibrium problems; Regularized variational inequalities; uniformly r-prox regular sets; nonconvex sets; iterative methods; convergence analysis; Banach spaces;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 A. S. Antipin, Iterative gradient prediction-type methods for computing fixed point of extremal mappings, In: J. Guddat, H. Th. Jonden, F. Nizicka, G. Still, F. Twitt (eds) Parametric Optimization and Related Topics IV[C], pp. 11-24. Peter Lang, Frankfurt (1997).
2 C. Baiocchi and A. Capelo, Variational and Quasi Variational Inequalities, John Wiley and Sons, New York, 1984.
3 E. Blum and W. Oettli, From optimization and variational inequalities to equilibrium problems, Math. Student 63 (1994), 123-145.
4 X. P. Ding, Auxiliary principle and algorithm for mixed equilibrium problems and bilevel mixed equilibrium problems in Banach spaces, J. Optim. Theory Appl. 146 (2010), 347-357, Doi 10.1007/s10957-010-9651-z.   DOI
5 F. H. Clarke, Y. S. Ledyaev, R. J. Stern and P. R.Wolenski, Nonsmooth Analysis and Control Theory, Springer-Verlag, New York, NY, 1998.
6 F. Giannessi and A. Maugeri, Variational Inequalities and Network Equilibrium Problems, Kluwer Acad. Pub. Dordrecht. 2000.
7 F. Giannessi, A. Maugeri and P. M. Pardalos, Equilibrium Problems:Nonsmooth Optimization and Variational Inequality Models, Kluwer Acad. Pub. Dordrecht. 2001.
8 R. Glowinski, J. L. Lion and R. Tremolieres, Numerical Analysis of Variational Inequalities, North Holland, Amsterdam, Holland 1981.
9 J. K. Kim, A. Farajzadeh and Salahuddin, New systems of extended nonlinear regularized nonconvex set valued variational inequalities, Communication on Applied Nonlinear Analysis 21 (3) (2014), 21-40.
10 M. A. Noor, Regularized mixed quasi equilibrium problems, J. Appl. Math. Comput. 23(2007), 183-191.   DOI
11 R. A. Poliquin, R. T. Rockafellar and L. Thibault, Local differentiability of distance functions, Trans. Amer. Math. Soc. 352 (2000), 5231-5249.   DOI
12 Salahuddin, Nonlinear regularized nonconvex random variational inequalities with fuzzy event in q-uniformly smooth Banach space, J. Applied Functional Analysis 10 (1-2) (2015), 40-52.
13 R. U. Verma and Salahuddin, A new class of nonlinear regularized nonconvex system of variational inequalities in Banach spaces, Transactions on Mathematical Programming and Applications 2 (5) (2014), 1-14.
14 W. Takahashi, Nonlinear variational inequalities and fixed point theorems, J. Math. Soc. Japan. 28 (1976), 168-181.   DOI
15 H. -K. Xu, Inequalities in Banach spaces with applications, Nonlinear Analysis, TMA, 16 (12) (1991), 1127-1138.   DOI