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A new iterative scheme for fixed point problems of infinite family of κ i -pseudo contractive mappings, equilibrium problem, variational inequality problems

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Abstract

In this paper, we modify the set of variational inequality to construct a new iterative scheme for finding a common element of the set of fixed point problems of infinite family of κ i -pseudo-contractive mappings and the set of equilibrium problem and two set of variational inequality problems.

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References

  1. Iiduka, H., Takahashi, W.: Weak convergence theorem by Ces‘aro means for nonexpansive mappings and inverse-strongly monotone mappings. J. Nonlinear Convex Anal., 7105–113 (2006)

  2. Kinderlehrer D., Stampaccia G.: An Iteration to Variational Inequalities and Their Applications. Academic Press, New York (1990)

    Google Scholar 

  3. Lions J.L., Stampacchia G.: Variational inequalities. Comm. Pure Appl. Math. 20, 493–517 (1967)

    Article  Google Scholar 

  4. Xu H.K.: Viscosity approximation methods for nonexpansive mappings. J. Math. Anal. Appl. 298, 279–291 (2004)

    Article  Google Scholar 

  5. Qin X., Shang M., Suc Y.: Strong convergence of a general iterative algorithm for equilibrium problems and variational inequality problems. Math. Comput. Model. 48, 1033–1046 (2008)

    Article  Google Scholar 

  6. Chang S.S., Lee H.W.J., Chan C.K.: A new method for solving equilibrium problem fixed point problem and variational inequality problem with application to optimization. Nonlinear Anal 70, 3307–3319 (2009)

    Article  Google Scholar 

  7. Hu C.S., Cai G.: Viscosity approximation schemes for fixed point problems and equilibrium problems and variational inequality problems. Nonlinear Anal 72, 1792–1808 (2010)

    Article  Google Scholar 

  8. Kangtunyakarn, A.: A New Iterative Algorithm for the Set of Fixed-Point Problems of Nonexpansive Mappings and the Set of Equilibrium Problem and Variational Inequality Problem, Abstract and Applied Analysis, vol. 2011, Article ID 562689, p. 24. doi:10.1155/2011/562689

  9. Qin X., Shang M., Zhou H.: Strong convergence of a general iterative method for variational inequality problems and fixed point problems in Hilbert spaces. Appl. Math. Comput. 200, 242–253 (2008)

    Article  Google Scholar 

  10. Takahashi W.: Nonlinear Functional Analysis. Yokohama Publishers, Yokohama (2000)

    Google Scholar 

  11. Xu H.K.: An iterative approach to quadratic optimization. J. Optim. Theory Appl. 116(3), 659–678 (2003)

    Article  Google Scholar 

  12. Xu H.K.: An iterative approach to quadratic optimization. J. Optim. Theory Appl. 116, 659–678 (2003)

    Article  Google Scholar 

  13. Marino G., Xu H.K.: Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces. J. Math. Anal. Appl. 329, 336–346 (2007)

    Article  Google Scholar 

  14. Blum E., Oettli W.: From optimization and variational inequalities to equilibrium problems. Math. Stud. 63, 123–145 (1994)

    Google Scholar 

  15. Combettes P.L., Hirstoaga A.: Equilibrium programming in Hilbert spaces. J. Nonlinear Convex Anal. 6, 117–136 (2005)

    Google Scholar 

  16. Kangtunyakarn A.: Strong convergence theorem for a generalized equilibrium problem and system of variational inequalities problem and infinite family of strict pseudo-contractions. Fix Point Theory Appl 2011(23), 1–16 (2011)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, 10520, Thailand

    Atid Kangtunyakarn

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  1. Atid Kangtunyakarn
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Correspondence to Atid Kangtunyakarn.

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Kangtunyakarn, A. A new iterative scheme for fixed point problems of infinite family of κ i -pseudo contractive mappings, equilibrium problem, variational inequality problems. J Glob Optim 56, 1543–1562 (2013). https://doi.org/10.1007/s10898-012-9925-0

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  • DOI: https://doi.org/10.1007/s10898-012-9925-0

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