Original Research Open access Published: 28 Jul 2026

Applications of Adjoint Operator

Quratulain, Zunaira Liaqat, Usman Munir, Raazia Bushra

Department of Mathematics, University of Management and Technology, Lahore, Pakistan.

Journal of Computational Mathematics and Physics volume 1 pages 43-57 (2026)

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Received 29 Apr 2026 Revised 16 Jul 2026 Accepted 22 Jul 2026 Published 28 Jul 2026 License CC BY 4.0

Keywords: Adjoint Operators; Reflexive Banach Spaces; Weak* Topology; Inverse Problems; Optimal Control Theory; Deep Learning and Backpropagation.

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Quratulain, Liaqat, Z., Munir, U. et al. Applications of Adjoint Operator. J. Comp. Math. Phy. 1, 43–57 (2026). http://jcmp.org/articles/2026-1-1-004

Quratulain, Liaqat, Z., Munir, U., & Bushra, R. (2026). Applications of Adjoint Operator. Journal of Computational Mathematics and Physics, 1(1), 43–57. http://jcmp.org/articles/2026-1-1-004

Quratulain, et al.. "Applications of Adjoint Operator." Journal of Computational Mathematics and Physics, vol. 1, no. 1, 2026, pp. 43–57, http://jcmp.org/articles/2026-1-1-004.

Quratulain, Zunaira Liaqat, Usman Munir, et al.. "Applications of Adjoint Operator." Journal of Computational Mathematics and Physics 1, no. 1 (2026): 43–57. http://jcmp.org/articles/2026-1-1-004.

Quratulain, Liaqat Z, Munir U, Bushra R. Applications of Adjoint Operator. J. Comp. Math. Phy.. 2026;1(1):43-57. Available from: http://jcmp.org/articles/2026-1-1-004

@article{uratulain2026applicationsof,
  title = {Applications of Adjoint Operator},
  author = {Quratulain and Liaqat, Zunaira and Munir, Usman and Bushra, Raazia},
  journal = {Journal of Computational Mathematics and Physics},
  year = {2026},
  volume = {1},
  number = {1},
  pages = {43--57},
  url = {http://jcmp.org/articles/2026-1-1-004},
}