Korean J. Math.  Vol 24, No 2 (2016)  pp.181-198
DOI: https://doi.org/10.11568/kjm.2016.24.2.181

System of generalized nonlinear regularized nonconvex variational inequalities

Salahuddin .

Abstract


In this work, we suggest a new it system of generalized nonlinear regularized nonconvex variational inequalities in a real Hilbert space and establish an equivalence relation between this system and fixed point problems. By using the equivalence relation we suggest a new perturbed projection iterative algorithms with mixed errors for finding a solution set of system of generalized nonlinear regularized nonconvex variational inequalities.

Keywords


System of generalized nonlinear regularized nonconvex variational inequalities, uniformly $r$-prox-regular sets, $(\kappa,\lambda)$-relaxed cocoercive mapping, inversely $\gamma$-strongly monotone mapping, strongly monotone mapping, iterative sequences, a

Subject classification

49J40, 47H06.

Sponsor(s)



Full Text:

PDF

References


M. K. Ahmad and Salahuddin, Perturbed three step approximation process with errors for a general implicit nonlinear variational inequalities, Int. J. Math. Math. Sci., Article ID 43818, (2006), 1-14. (Google Scholar)

M. K. Ahmad and Salahuddin, A stable perturbed algorithms for a new class of generalized nonlinear implicit quasi variational inclusions in Banach spaces, Advances in Pure Mathematics 2 (2) (2012), 139–148. (Google Scholar)

S. S. Chang, H. W. J. Lee and C. K. Chan, Generalized system for relaxed cocoercive variational inequalities in Hilbert space, Applied Math. Lett. 20 (3) (2007), 329–334. (Google Scholar)

F. H. Clarke, Optimization and nonsmooth analysis, Wiley Int. Science, New York, 1983. (Google Scholar)

F. H. Clarke, Y. S. Ledyaw, R. J. Stern and P. R. Wolenski, Nonsmooth analysis and control theory, Springer-Verlag, New York 1998. (Google Scholar)

X. P. Ding, Existence and algorithm of solutions for a system of generalized mixed implicit equilibrium problem in Banach spaces, Appl. Math. Mech. 31 (9) (2010), 1049–1062. (Google Scholar)

M. C. Ferris and J. S. Pang, Engineering and economic applications of comple- mentarity problems, SIAM Review 39 (4) (1997), 669–713. (Google Scholar)

N. J. Huang and Y. P. Fang, Generalized m-accretive mappings in Banach spaces, J. Sichuan University 38 (4) (2001), 591–592. (Google Scholar)

I. Inchan and N. Petrot, System of general variational inequalities involv- ing different nonlinear operators related to fixed point problems and its ap- plications, Fixed point Theory, Vol. 2011, Article ID 689478, pages 17, doi 10.1155/2011/689478. (Google Scholar)

J. K. Kim, Salahuddin and A. Farajzadeh, A new system of extended nonlin- ear regularized nonconvex set valued variational inequalities, Commun. Appl. Nonlinear Anal. 21 (3) (2014), 21–28. (Google Scholar)

M. M. Jin, Iterative algorithms for a new system of nonlinear variational inclu- sions with (A,η)-accretive mappings in Banach spaces, Comput. Math. Appl. 54 (2007), 579–588. (Google Scholar)

B. S. Lee and Salahuddin, A general system of regularized nonconvex variational inequalities, Appl. Comput. Math. 3 (4) (2014), 1–7. (Google Scholar)

B. S. Lee, M. F. Khan and Salahuddin, Generalized Nonlinear Quasi-Variational Inclusions in Banach Spaces, Comput. Maths. Appl 56 (5) (2008), 1414–1422. (Google Scholar)

H. Y. Lan, N. J. Huang and Y. J. Cho, New iterative approximation for a system of generalized nonlinear variational inclusions with set valued mappings in Banach spaces, Math. Inequal. Appl. 1 (2006), 175–187. (Google Scholar)

S.B. Nadler, Multi-valued contraction mappings, Pacific J. Math. 30 (1969) 475– 488. (Google Scholar)

G. Stampacchia, An Formes bilineaires coercitives sur les ensembles convexes, C. R. Acad. Sci. Paris 258 (1964), 4413–4416. (Google Scholar)

R. A. Poliquin, R. T. Rockafellar and L. Thibault, Local differentiability of distance functions, Trans. Amer. Math. Soc. 352 (2000), 5231–5249. (Google Scholar)

R. U. Verma, Projection methods, and a new system of cocoercive variational inequality problems, Int. J. Diff. Equa. Appl. 6 (3) (2002), 359–367. (Google Scholar)

R. U. Verma, Generalized system for relaxed cocoercive variational inequalities and projection methods, J. Optim. Theo. Appl. 121 (2004), 203–210. (Google Scholar)

D. J. Wen, Projection methods for a generalized system of nonconvex variational inequalities with different nonlinear operators, Nonlinear Anal. 73 (2010), 2292– 2297. (Google Scholar)

X. Weng, Fixed point iteration for local strictly pseudo contractive mapping, Proceedings of American Mathematical Society 113 (3) (1991), 727–737. (Google Scholar)


Refbacks

  • There are currently no refbacks.


ISSN: 1976-8605 (Print), 2288-1433 (Online)

Copyright(c) 2013 By The Kangwon-Kyungki Mathematical Society, Department of Mathematics, Kangwon National University Chuncheon 21341, Korea Fax: +82-33-259-5662 E-mail: kkms@kangwon.ac.kr