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Minimization of Quadratic Functionals Through Γ-Hilbert Space

Year 2022, Volume: 19 Issue: 1, 22 - 28, 01.05.2022

Sahın Injamamul Islam Nırmal Sarkar Ashoke Das

Abstract

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.

References

  • T. E. Aman and D. K. Bhattacharya, "Γ-Hilbert Space and linear quadratic control problem," Revista de la Academia Canaria de Ciencias, vol. 15, no. 1-2, pp. 107-114, 2004.
  • A. Gosh, A. Das and T. E. Aman, "Representation Theorem on Γ-Hilbert Space," International Journal of Mathematics Trends and Technology, vol. 52, no. 9, pp. 608-615, 2017.
  • 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.
  • A. Das, A. Ghosh and T. E. Aman, "Calculas on Γ-Hilbert Space," Journal of Interdisciplinary Cycle Research. vol. 12, no. 7, pp. 254-268, 2020.

Year 2022, Volume: 19 Issue: 1, 22 - 28, 01.05.2022

Sahın Injamamul Islam Nırmal Sarkar Ashoke Das

Abstract

References

  • T. E. Aman and D. K. Bhattacharya, "Γ-Hilbert Space and linear quadratic control problem," Revista de la Academia Canaria de Ciencias, vol. 15, no. 1-2, pp. 107-114, 2004.
  • A. Gosh, A. Das and T. E. Aman, "Representation Theorem on Γ-Hilbert Space," International Journal of Mathematics Trends and Technology, vol. 52, no. 9, pp. 608-615, 2017.
  • 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.
  • A. Das, A. Ghosh and T. E. Aman, "Calculas on Γ-Hilbert Space," Journal of Interdisciplinary Cycle Research. vol. 12, no. 7, pp. 254-268, 2020.
There are 4 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Sahın Injamamul Islam 0000-0002-8587-7922

Nırmal Sarkar 0000-0002-9050-1479

Ashoke Das 0000-0002-6612-0182

Publication Date May 1, 2022
Published in Issue Year 2022 Volume: 19 Issue: 1

Cite

APA Islam, S. I., Sarkar, N., & Das, A. (2022). Minimization of Quadratic Functionals Through Γ-Hilbert Space. Cankaya University Journal of Science and Engineering, 19(1), 22-28.
AMA Islam SI, Sarkar N, Das A. Minimization of Quadratic Functionals Through Γ-Hilbert Space. CUJSE. May 2022;19(1):22-28.
Chicago Islam, Sahın Injamamul, Nırmal Sarkar, and Ashoke Das. “Minimization of Quadratic Functionals Through Γ-Hilbert Space”. Cankaya University Journal of Science and Engineering 19, no. 1 (May 2022): 22-28.
EndNote Islam SI, Sarkar N, Das A (May 1, 2022) Minimization of Quadratic Functionals Through Γ-Hilbert Space. Cankaya University Journal of Science and Engineering 19 1 22–28.
IEEE S. I. Islam, N. Sarkar, and A. Das, “Minimization of Quadratic Functionals Through Γ-Hilbert Space”, CUJSE, vol. 19, no. 1, pp. 22–28, 2022.
ISNAD Islam, Sahın Injamamul et al. “Minimization of Quadratic Functionals Through Γ-Hilbert Space”. Cankaya University Journal of Science and Engineering 19/1 (May 2022), 22-28.
JAMA Islam SI, Sarkar N, Das A. Minimization of Quadratic Functionals Through Γ-Hilbert Space. CUJSE. 2022;19:22–28.
MLA Islam, Sahın Injamamul et al. “Minimization of Quadratic Functionals Through Γ-Hilbert Space”. Cankaya University Journal of Science and Engineering, vol. 19, no. 1, 2022, pp. 22-28.
Vancouver Islam SI, Sarkar N, Das A. Minimization of Quadratic Functionals Through Γ-Hilbert Space. CUJSE. 2022;19(1):22-8.