Variational Inequality In Hilbert Spaces And Their Applications

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ABSTRACT

The study of variational inequalities frequently deals with a mapping F from a vector space X or a convex subset of X into its dual X 0 . Let H be a real Hilbert space and a(u, v) be a real bilinear form on H. Assume that the linear and continuous mapping A : H −→ H 0 determines a bilinear form via the pairing a(u, v) = hAu, vi. Given K ⊂ H and f ∈ H 0 . Then, Variational inequality(VI) is the problem of finding u ∈ K such that a(u, v − u) ≥ hf, v − ui, for all v ∈ K. In this work, we outline some results in theory of variational inequalities. Their relationships with other problems of Nonlinear Analysis and some applications are also discussed

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APA

Izuchukwu, U (2021). Variational Inequality In Hilbert Spaces And Their Applications. Afribary. Retrieved from https://afribary.com/works/variational-inequality-in-hilbert-spaces-and-their-applications

MLA 8th

Izuchukwu, Udeani "Variational Inequality In Hilbert Spaces And Their Applications" Afribary. Afribary, 16 Apr. 2021, https://afribary.com/works/variational-inequality-in-hilbert-spaces-and-their-applications. Accessed 29 Mar. 2024.

MLA7

Izuchukwu, Udeani . "Variational Inequality In Hilbert Spaces And Their Applications". Afribary, Afribary, 16 Apr. 2021. Web. 29 Mar. 2024. < https://afribary.com/works/variational-inequality-in-hilbert-spaces-and-their-applications >.

Chicago

Izuchukwu, Udeani . "Variational Inequality In Hilbert Spaces And Their Applications" Afribary (2021). Accessed March 29, 2024. https://afribary.com/works/variational-inequality-in-hilbert-spaces-and-their-applications