A NEW SYMMETRIC DIFFERENTIAL OPERATOR OF NORMALIZED FUNCTIONS WITH APPLICATIONS IN IMAGE PROCESSING
DOI:
https://doi.org/10.4314/jfas.v12i2.22Keywords:
fractional calculus; subordination and superordination; differential operator; unit disk; analytic function; subordination; fractional operator; univalent function.Abstract
Recently, a symmetric differential operator (SDO) is attracted to studying in the field of mathematical analysis. A new formal of SDO is presented to generalize some well known differential operators in a complex domain. According to this formulation, we shall exam the boundedness and compactness of this operator in complex spaces, such as Hilbert space and Sobolev space. For this purpose, we suggest new norms to solve the fractional Beltrami equation in the open unit disk. This operator has ability to depict the analytic geometric representation of the solution of second order differential equation utilizing the concept of Schwarzian derivative in the open unit disk. Applications in imagings are given the sequel.
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References
[1] S. Klimentov, Representations of the “second kind” for the Hardy classes of solutions to
the Beltrami equation, Siberian Mathematical Journal,2014, (55.2),262–275.
[2] Sàlàgean G S, Subclasses of univalent functions, Complex Analysis-Fifth Romanian-
Finnish Seminar, Part 1 (Bucharest, 1981), Lecture Notes in Math., 1983, (1013), 362–372.
[3] Ibrahim R W, Darus M, Subordination inequalities of a new Salagean-difference operator, International Journal of Mathematics and Computer Science 2019, (14.3), 573-582.
[4] Ibrahim R W, New classes of analytic functions determined by a modified differential-difference operator in a complex domain, Karbala International Journal of Modern Science ,2017, (3), 53–58.
[5] Ibrahim R W, Darus M, New symmetric differential and integral operators defined in the complex domain, Symmetry, 2019, 1–12.
[6] Lehto O, Univalent functions and Teichmüller spaces, Springer-Verlag, 1987, 50-59.
[7] Dunkl C F, Differential-difference operators associated with reflections groups,
Trans. Am. Math. Soc., 1989, (311),167–183.
[8] Ibrahim R W, Arched foot based on conformal complex neural network testing,
Mathematics and Computers in Simulation, 2020, (174), 175-182.
the Beltrami equation, Siberian Mathematical Journal,2014, (55.2),262–275.
[2] Sàlàgean G S, Subclasses of univalent functions, Complex Analysis-Fifth Romanian-
Finnish Seminar, Part 1 (Bucharest, 1981), Lecture Notes in Math., 1983, (1013), 362–372.
[3] Ibrahim R W, Darus M, Subordination inequalities of a new Salagean-difference operator, International Journal of Mathematics and Computer Science 2019, (14.3), 573-582.
[4] Ibrahim R W, New classes of analytic functions determined by a modified differential-difference operator in a complex domain, Karbala International Journal of Modern Science ,2017, (3), 53–58.
[5] Ibrahim R W, Darus M, New symmetric differential and integral operators defined in the complex domain, Symmetry, 2019, 1–12.
[6] Lehto O, Univalent functions and Teichmüller spaces, Springer-Verlag, 1987, 50-59.
[7] Dunkl C F, Differential-difference operators associated with reflections groups,
Trans. Am. Math. Soc., 1989, (311),167–183.
[8] Ibrahim R W, Arched foot based on conformal complex neural network testing,
Mathematics and Computers in Simulation, 2020, (174), 175-182.
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Published
2020-04-29
How to Cite
IBRAHIM, R. W. A NEW SYMMETRIC DIFFERENTIAL OPERATOR OF NORMALIZED FUNCTIONS WITH APPLICATIONS IN IMAGE PROCESSING. Journal of Fundamental and Applied Sciences, [S. l.], v. 12, n. 2, p. 852–864, 2020. DOI: 10.4314/jfas.v12i2.22. Disponível em: https://jfas.info/index.php/JFAS/article/view/551. Acesso em: 30 jan. 2025.
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