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Variational Inequalities in Semi-inner Product Spaces

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Computational Mathematics and Variational Analysis

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 159))

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.

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Author information

Authors and Affiliations

  1. Dhirubhai Ambani Institute of Information and Communication Technology, Gandhinagar, India

    Nabin K. Sahu

  2. Dept. of Economics, Ibn Zohr University, Agadir, Morocco

    Ouayl Chadli

  3. Dept. of Mathematics, University of Central Florida, Orlando, FL, USA

    R. N. Mohapatra

Authors
  1. Nabin K. Sahu
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  2. Ouayl Chadli
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  3. R. N. Mohapatra
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Hellenic Military Academy, Vari Attikis, Greece

    Nicholas J. Daras

  2. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

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Sahu, N.K., Chadli, O., Mohapatra, R.N. (2020). Variational Inequalities in Semi-inner Product Spaces. In: Daras, N., Rassias, T. (eds) Computational Mathematics and Variational Analysis. Springer Optimization and Its Applications, vol 159. Springer, Cham. https://doi.org/10.1007/978-3-030-44625-3_23

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