1
Department of Mathematics, College of Education for Pure Sciences, the University of Babylon, Iraq
(pure.aday.saheb@uobabylon.edu.iq)
2
Department of Mathematics and computer applications, College of Science, Al Muthanna University, Iraq
(Sci.rafid@mu.edu.iq)
Abstract :
In our work, we introduced a distinct subclass of univalent harmonic functions referred to as a subclass of chiral functions. These functions are defined by combining the generalized Komatu operator with the integral operator (R − K), which has positive coefficients within the unit disc A. Also, we generalize the same subclass into neutrosophic complex numbers. Throughout our investigation, we establish several properties associated with these functions, including coefficient estimates, the convex formula, the integral operator, and the Hadamard product. On the other hand, we present the Neutrosophic convex formula and the neutrosophic integral operator.
Keywords :
Spiral-like functions generalized integral operator; sufficient coefficient , convex combination; neutrosophic complex numbers; neutrosophic convex formula.
References :
[1] Robertson, M. S.” Radii of starlikeness and close-to-convexity”, Proc. Amer. Math. Soc. 16, 847- 852. (1965).
[2] Spacek, L.” Contribution a la th´eorie des fonctions univalentes”, C asopis pest. Mat. 62, 12- 19.(1932).
[3] Zamorski, J.” About the extremal sprial schlicht functions”, Ann. Polon. Math. 9, 265-273.(1962).
[4] Buti, R., H. and Jassim, K., A.” A subclass Of spiral – like functions defined by generalized komatu operator with (R-K) integral operator”, IOP Conf. Ser.: Mater. Sci. Eng. 571 012040. (2019).
[5] Komatu, Y.” On analytic prolongation of a family of integral operators”, Mathematica (Cluj), 32 (55), 141-145.(1990).
[6] Y. Avcı and E. Złotkiewicz, “On harmonic univalent mappings”, Annales Universitatis Mariae Curie-Skłodowska A, vol. 44, pp. 1–7, (1990).
[7] J. Clunie and T. Sheil-Small, “Harmonic univalent functions,” Annales Academiae Scientiarum Fennicae A, vol. 9, pp. 3–25, (1984).
[8] Bharavi,S.R. and Haripriya, M.” On a class of a-convex functions subordinate to a shall shaped region”J. Analysis, 25: 99-105.( 2017).
[9] Libera, R.J.” Some Classes of Regular Univalent Funtions”, Proc. Am. Math. Soc, 16: 755- 758.( 1965).
[10] M. Abobala and A. Hatip, "An Algebraic Approach to Neutrosophic Euclidean Geometry," Neutrosophic Sets and Systems, vol. 43, pp. 114-123, 2021.
[11] M. B. Zeina and M. Abobala, "A Novel Approach of Neutrosophic Continuous Probability Distributions using AH-Isometry used in Medical Applications," in Cognitive Intelligence with Neutrosophic Statistics in Bioinformatics, Elsevier, 2023.
[12] M. Ibrahim. A. Agboola, B.Badmus and S. Akinleye. On refined Neutrosophic Vector Spaces, International Journal of Neutrosophic Science, Vol. 7, 2020, pp. 97-109.
[13] Abobala, M., Bal, M., Aswad, M., "A Short Note On Some Novel Applications of Semi Module Homomorphisms", International journal of neutrosophic science, 2022.
[14] M. Bisher Zeina and M. Abobala, “On The Refined Neutrosophic Real Analysis Based on Refined Neutrosophic Algebraic AH-Isometry,” Neutrosophic Sets and Systems, vol. 54, 2023.
[15] Ben Othman, K., Von Shtawzen, O., Khaldi, A., and Ali, R., "On The Symbolic 8-Plithogenic Matrices", Pure Mathematics For Theoretical Computer Science, Vol.1, 2023.
| Style | # |
|---|---|
| MLA | Audy Hatim Saheb, Rafid Habib Buti. "A Specific Category of Harmonic Functions Characterized By A Generalized Komatu Operator in Conjunction With The (R-K) Integral Operator and Applications to Neutrosophic Complex Field." International Journal of Neutrosophic Science, Vol. 23, No. 3, 2024 ,PP. 44-50 (Doi : https://doi.org/10.54216/IJNS.230304) |
| APA | Audy Hatim Saheb, Rafid Habib Buti. (2024). A Specific Category of Harmonic Functions Characterized By A Generalized Komatu Operator in Conjunction With The (R-K) Integral Operator and Applications to Neutrosophic Complex Field. Journal of International Journal of Neutrosophic Science, 23 ( 3 ), 44-50 (Doi : https://doi.org/10.54216/IJNS.230304) |
| Chicago | Audy Hatim Saheb, Rafid Habib Buti. "A Specific Category of Harmonic Functions Characterized By A Generalized Komatu Operator in Conjunction With The (R-K) Integral Operator and Applications to Neutrosophic Complex Field." Journal of International Journal of Neutrosophic Science, 23 no. 3 (2024): 44-50 (Doi : https://doi.org/10.54216/IJNS.230304) |
| Harvard | Audy Hatim Saheb, Rafid Habib Buti. (2024). A Specific Category of Harmonic Functions Characterized By A Generalized Komatu Operator in Conjunction With The (R-K) Integral Operator and Applications to Neutrosophic Complex Field. Journal of International Journal of Neutrosophic Science, 23 ( 3 ), 44-50 (Doi : https://doi.org/10.54216/IJNS.230304) |
| Vancouver | Audy Hatim Saheb, Rafid Habib Buti. A Specific Category of Harmonic Functions Characterized By A Generalized Komatu Operator in Conjunction With The (R-K) Integral Operator and Applications to Neutrosophic Complex Field. Journal of International Journal of Neutrosophic Science, (2024); 23 ( 3 ): 44-50 (Doi : https://doi.org/10.54216/IJNS.230304) |
| IEEE | Audy Hatim Saheb, Rafid Habib Buti, A Specific Category of Harmonic Functions Characterized By A Generalized Komatu Operator in Conjunction With The (R-K) Integral Operator and Applications to Neutrosophic Complex Field, Journal of International Journal of Neutrosophic Science, Vol. 23 , No. 3 , (2024) : 44-50 (Doi : https://doi.org/10.54216/IJNS.230304) |