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Variational Inequalities in Semi-inner Product Spaces

In: Computational Mathematics and Variational Analysis

Author

Listed:
  • Nabin K. Sahu

    (Dhirubhai Ambani Institute of Information and Communication Technology)

  • Ouayl Chadli

    (Ibn Zohr University)

  • R. N. Mohapatra

    (University of Central Florida)

Abstract

Variational Inequalities play an important role in solving many outstanding problems ranging from Mechanics, Physics, Engineering, and Economics. The work of the Italian and French mathematicians laid a solid mathematical foundation and today, it is an interesting area of considerable research activity. The variational inequalities were first considered in Hilbert spaces and subsequently to Banach spaces. In 1961, Lumer introduced the theory of semi-inner product spaces. This was followed by the work of Giles and many other researchers. In this paper, we have mentioned most of the results in variational inequalities in semi-inner product spaces. The new results proved in this paper are for a system of variational inequalities in a semi-inner product space. These results throw a light into the structural study of variational inequalities in uniformly smooth Banach spaces.

Suggested Citation

  • Nabin K. Sahu & Ouayl Chadli & R. N. Mohapatra, 2020. "Variational Inequalities in Semi-inner Product Spaces," Springer Optimization and Its Applications, in: Nicholas J. Daras & Themistocles M. Rassias (ed.), Computational Mathematics and Variational Analysis, pages 421-439, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-44625-3_23
    DOI: 10.1007/978-3-030-44625-3_23
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    Keywords

    47H04; 47J20; 49J40; 47H10;
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