Minimization of Quadratic Functionals Through Γ-Hilbert Space
Minimization of Quadratic Functionals Through Γ-Hilbert Space
In this article we introduce the Gateaux differential and Frechet differential in Γ-Hilbert
space. We show the examples and related theorems in this space. We have noticed that
two differentials mentioned above will be equal for certain condition. Also, we discuss
the relative extremum and the stationary point of a functional in Γ-Hilbert space. We
already investigated the characteristics of both bounded and unbounded operators of
Γ-Hilbert space. Now, by using previous concept we elaborate optimization problems
and extremum of quadratic functionals in Γ-Hilbert space. Here we observe that how
the function of the solution of a operator equation minimizes the quadratic functionals.
Finally we describe the Minimization of quadratic functionals and its related theorem
via Γ-Hilbert space.
Keywords:
Γ-Hilbert space, Gateaux Γ-derivative, Frechet Γ-derivative Relative extremum, Stationary point, Quadratic functionals.,
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- S. Islam and A. Das, "On Some bounded Operators and their characterizations in Γ-Hilbert Space," Cumhuriyet Science Journal, vol. 41, no. 4, pp. 854-861, 2020.
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- Yayın Aralığı: Yılda 2 Sayı
- Başlangıç: 2009
- Yayıncı: Çankaya Üniversitesi
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Minimization of Quadratic Functionals Through Γ-Hilbert Space