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Year 2016, Volume: 4 Issue: 4, 33 - 41, 31.12.2016

Rais Ahmad Haider Abbas Rizvi Adem Kilicman

Abstract

References

  • A. Moudafi, Mixed equilibrium problems: Sensitivity analysis and algorithmic aspect, Computers and Mathematics with applications (2002), Vol. 44,1099-1108.
  • E. Blum, W. Oettli, From optimization and variational inequalities to equilibrium problems, Math. student, 63(1994),pp. 123-145.
  • F. Giannessi and A. Maugeri, Variational inequalities and Network equilibrium problems, Plenum Press, New york, 1995.
  • F. Giannessi (Ed.), Vector variational inequalities and Vector Equilibria, Math. Theories Nonconvex Optim. Appl., vol.38, Kluwer Academic Publishers, Dordrecht (2000).
  • X.P. Ding, Quasi-equilibrium problems in noncompact generalized convex spaces, Applied Mathematics and Mechanics, June 2000, Volume 21, Issue 6, pp 637-644.
  • X.P. Ding Quasi-equilibrium problems with applications to finite optimization and constrained games in general topologies spaces, Appl. Math. Lett., 13(2000), pp.21-26.
  • M.A. Noor, Oettli W. On general nonlinear complementarity problems and quasi-equilibria Mathematiche(Catania), 49(1964), pp.313-331.
  • M.A. Noor, Multivalued general equilibrium problems, Journal of Mathematical Analysis and Applications, Vol. 283, issue 1, 1 july 2003, pages 140-149.
  • X.P. Ding, Iterative algorithm of solutions for generalized mixed implicit equilibrium-like problems. Appl. Math. Comput., 162, 799-809(2005).
  • B.S. Lee and Salahuddin, Existence theorem for vector quasi variational like inequalities, J. Nonlinear Analysis Appl., Vol. 2011, Art ID jnaa 00121,1-9.
  • N.K. Mahato and C. Nahak, Equilibrium problems with generalized relaxed monotonicities in Banach spaces, Opsearch, DOI.10.1007/s12597-0(2013).

Iterative Algorithm for extended mixed equilibrium problem

Year 2016, Volume: 4 Issue: 4, 33 - 41, 31.12.2016

Rais Ahmad Haider Abbas Rizvi Adem Kilicman

Abstract

In this paper, we introduce and study an extended mixed equilibrium problem by using auxiliary principle technique. A generalized predictor-corrector iterative algorithm is defined for solving extended mixed equilibrium problem. The convergence of the method mentioned requires some condition (∗), g-relatively relaxed Lipschitz continuity and relatively g-relaxed monotonicity of the mappings.

Keywords

Equilibrium algorithm relatively-relaxed auxiliary principle

References

  • A. Moudafi, Mixed equilibrium problems: Sensitivity analysis and algorithmic aspect, Computers and Mathematics with applications (2002), Vol. 44,1099-1108.
  • E. Blum, W. Oettli, From optimization and variational inequalities to equilibrium problems, Math. student, 63(1994),pp. 123-145.
  • F. Giannessi and A. Maugeri, Variational inequalities and Network equilibrium problems, Plenum Press, New york, 1995.
  • F. Giannessi (Ed.), Vector variational inequalities and Vector Equilibria, Math. Theories Nonconvex Optim. Appl., vol.38, Kluwer Academic Publishers, Dordrecht (2000).
  • X.P. Ding, Quasi-equilibrium problems in noncompact generalized convex spaces, Applied Mathematics and Mechanics, June 2000, Volume 21, Issue 6, pp 637-644.
  • X.P. Ding Quasi-equilibrium problems with applications to finite optimization and constrained games in general topologies spaces, Appl. Math. Lett., 13(2000), pp.21-26.
  • M.A. Noor, Oettli W. On general nonlinear complementarity problems and quasi-equilibria Mathematiche(Catania), 49(1964), pp.313-331.
  • M.A. Noor, Multivalued general equilibrium problems, Journal of Mathematical Analysis and Applications, Vol. 283, issue 1, 1 july 2003, pages 140-149.
  • X.P. Ding, Iterative algorithm of solutions for generalized mixed implicit equilibrium-like problems. Appl. Math. Comput., 162, 799-809(2005).
  • B.S. Lee and Salahuddin, Existence theorem for vector quasi variational like inequalities, J. Nonlinear Analysis Appl., Vol. 2011, Art ID jnaa 00121,1-9.
  • N.K. Mahato and C. Nahak, Equilibrium problems with generalized relaxed monotonicities in Banach spaces, Opsearch, DOI.10.1007/s12597-0(2013).
There are 11 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Rais Ahmad This is me

Haider Abbas Rizvi This is me

Adem Kilicman This is me

Publication Date December 31, 2016
Published in Issue Year 2016 Volume: 4 Issue: 4

Cite

APA Ahmad, R., Rizvi, H. A., & Kilicman, A. (2016). Iterative Algorithm for extended mixed equilibrium problem. New Trends in Mathematical Sciences, 4(4), 33-41.
AMA Ahmad R, Rizvi HA, Kilicman A. Iterative Algorithm for extended mixed equilibrium problem. New Trends in Mathematical Sciences. December 2016;4(4):33-41.
Chicago Ahmad, Rais, Haider Abbas Rizvi, and Adem Kilicman. “Iterative Algorithm for Extended Mixed Equilibrium Problem”. New Trends in Mathematical Sciences 4, no. 4 (December 2016): 33-41.
EndNote Ahmad R, Rizvi HA, Kilicman A (December 1, 2016) Iterative Algorithm for extended mixed equilibrium problem. New Trends in Mathematical Sciences 4 4 33–41.
IEEE R. Ahmad, H. A. Rizvi, and A. Kilicman, “Iterative Algorithm for extended mixed equilibrium problem”, New Trends in Mathematical Sciences, vol. 4, no. 4, pp. 33–41, 2016.
ISNAD Ahmad, Rais et al. “Iterative Algorithm for Extended Mixed Equilibrium Problem”. New Trends in Mathematical Sciences 4/4 (December2016), 33-41.
JAMA Ahmad R, Rizvi HA, Kilicman A. Iterative Algorithm for extended mixed equilibrium problem. New Trends in Mathematical Sciences. 2016;4:33–41.
MLA Ahmad, Rais et al. “Iterative Algorithm for Extended Mixed Equilibrium Problem”. New Trends in Mathematical Sciences, vol. 4, no. 4, 2016, pp. 33-41.
Vancouver Ahmad R, Rizvi HA, Kilicman A. Iterative Algorithm for extended mixed equilibrium problem. New Trends in Mathematical Sciences. 2016;4(4):33-41.