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Common Fixed Point Theorems in Topological Vector Spaces via Intersection Theorems

Author

Listed:
  • Ravi P. Agarwal

    (A&M University-Kingsville)

  • Mircea Balaj

    (University of Oradea)

  • Donal O’Regan

    (National University of Ireland Galway)

Abstract

Our purpose in this paper is to present two methods for obtaining common fixed point theorems in topological vector spaces. Both methods combine an intersection theorem and a fixed point theorem, but the order in which they are applied differs.

Suggested Citation

  • Ravi P. Agarwal & Mircea Balaj & Donal O’Regan, 2017. "Common Fixed Point Theorems in Topological Vector Spaces via Intersection Theorems," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 443-458, May.
    • Handle: RePEc:spr:joptap:v:173:y:2017:i:2:d:10.1007_s10957-017-1082-7
    DOI: 10.1007/s10957-017-1082-7
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    References listed on IDEAS

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    1. A. Daniilidis & N. Hadjisavvas, 1999. "Characterization of Nonsmooth Semistrictly Quasiconvex and Strictly Quasiconvex Functions," Journal of Optimization Theory and Applications, Springer, vol. 102(3), pages 525-536, September.
    2. D. Aussel & N. Hadjisavvas, 2004. "On Quasimonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 121(2), pages 445-450, May.
    3. R. P. Agarwal & M. Balaj & D. O’Regan, 2014. "A Common Fixed Point Theorem with Applications," Journal of Optimization Theory and Applications, Springer, vol. 163(2), pages 482-490, November.
    4. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, December.
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    Cited by:

    1. Mircea Balaj & Dan Florin Serac, 2023. "Generalized Equilibrium Problems," Mathematics, MDPI, vol. 11(9), pages 1-11, May.
    2. Mircea Balaj, 2021. "Intersection theorems for generalized weak KKM set‐valued mappings with applications in optimization," Mathematische Nachrichten, Wiley Blackwell, vol. 294(7), pages 1262-1276, July.
    3. Raúl Fierro, 2021. "An Intersection Theorem for Topological Vector Spaces and Applications," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 118-133, October.
    4. Ravi P. Agarwal & Mircea Balaj & Donal O’Regan, 2018. "Intersection Theorems with Applications in Optimization," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 761-777, December.

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