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Hierarchical Equilibrium and Generalized Variational Inequality Problems

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Transactions on Engineering Technologies

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 275))

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Abstract

In this paper, we study the convex feasibility problem (CFP) in the case that each is a solution set of the generalized variational inequality and the equilibrium problem and introduce a new approach method to find a common element in the intersection of the set of the solutions of a finite family of equilibrium problems and the intersection of the set of the solutions of a finite family of generalized variational inequality problems in a real Hilbert space which is a unique solution of the hierarchical equilibrium and generalized variational inequality problems(HEGVIP). Under appropriate conditions, some strong convergence theorems are established. Our results generalize and improve the corresponding results of Wairojjana and Kumam (2013) [27] and some authors.

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Acknowledgments

The authors were supported by the Higher Education Research Promotion and National Research University Project of Thailand, Office of the Higher Education Commission (Grant no. NRU56000508).

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Nopparat Wairojjana & Poom Kumam

Authors
  1. Nopparat Wairojjana
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  2. Poom Kumam
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Corresponding author

Correspondence to Poom Kumam .

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Editors and Affiliations

  1. Department of Multimedia Engineering College of Engineering, Mokpo National University, Chonnam, Korea, Republic of (South Korea)

    Gi-Chul Yang

  2. International Association of Engineers, Hong Kong, Hong Kong SAR

    Sio-Iong Ao

  3. Faculty of Information Sciences and Engineering, University of Canberra, Canberra, Aust Capital Terr, Australia

    Xu Huang

  4. Computer Sci. in the Graduate Division, Tijuana Institute of Technology, Tijuana, Baja California, Mexico

    Oscar Castillo

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Wairojjana, N., Kumam, P. (2014). Hierarchical Equilibrium and Generalized Variational Inequality Problems. In: Yang, GC., Ao, SI., Huang, X., Castillo, O. (eds) Transactions on Engineering Technologies. Lecture Notes in Electrical Engineering, vol 275. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7684-5_24

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  • DOI: https://doi.org/10.1007/978-94-007-7684-5_24

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-7683-8

  • Online ISBN: 978-94-007-7684-5

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