Variational Inequalities in Semi-inner Product Spaces

Nabin K. Sahu (), Ouayl Chadli () and R. N. Mohapatra ()
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Nabin K. Sahu: Dhirubhai Ambani Institute of Information and Communication Technology
Ouayl Chadli: Ibn Zohr University
R. N. Mohapatra: University of Central Florida

A chapter in Computational Mathematics and Variational Analysis, 2020, pp 421-439 from Springer

Abstract: 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.

Keywords: 47H04; 47J20; 49J40; 47H10 (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-44625-3_23

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DOI: 10.1007/978-3-030-44625-3_23

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