A Subclass of Harmonic Multivalent Functions Associated with Differential Operator
Abstract
In the present paper, we propose and study a new subclass of harmonic multivalent functions in the open unit disc $ U=\{z:z\in \mathbb{C},|z|<1\},$ which is characterized by its association with a special differential operator. This investigation focuses on establishing several fundamental properties of the introduced subclass including coefficient bounds, convex combination criteria, convolution conditions and the characterization of its extreme points.References
Ahuja, O. P., & Jahangiri, J. M. (2001). Multivalent harmonic starlike functions. Annales Universitatis Mariae Curie-Skłodowska, Sectio A, 55, 1–13.
Bernardi, S. D. (1969). Convex and starlike univalent functions. Transactions of the American Mathematical Society, 135, 429–446. https://doi.org/10.2307/1995025
Bobalade, D. D., Sangle, N. D., & Yadav, S. N. (2023). Subclass of harmonic univalent functions associated with the differential operator. Southeast Asian Bulletin of Mathematics, 47(2), 191–203.
Clunie, J., & Sheil-Small, T. (1984). Harmonic univalent functions. Annales Fennici Mathematici, 9(1), 3–25. https://doi.org/10.5186/aasfm.1984.0905
El-Ashwah, R. M., & Aouf, M. K. (2010). New classes of p-valent harmonic functions. Bulletin of Mathematical Analysis and Applications, 2(3), 53–64.
Ezhilarasi, R., Sudharsan, T. V., & Subramanian, K. G. (2014). A class of harmonic multivalent functions defined by an integral operator. General Mathematics Notes, 22(1), 17–30.
Jahangiri, J. M. (1999). Harmonic functions starlike in the unit disk. Journal of Mathematical Analysis and Applications, 235(2), 470–477. https://doi.org/10.1006/jmaa.1999.6377
Makinde, D. O. (2016). On a new differential operator. Theoretical Mathematics & Applications, 6(4), 71–74.
Makinde, D. O., & Afolabi, A. O. (2012). On a subclass of harmonic univalent functions. Transnational Journal of Science and Technology, 2(2), 1–11.
Seoudy, T. (2014). On a linear combination of classes of harmonic p-valent functions defined by certain modified operator. Bulletin of the Iranian Mathematical Society, 40(6), 1539–1551.
Sharma, R. B., & Ravinder, B. (2018). On a subclass of harmonic univalent functions. Journal of Physics: Conference Series, 1000, 012115. https://doi.org/10.1088/1742-6596/1000/1/012115
Yasar, E., & Yalçın, S. (2012). Properties of a subclass of multivalent harmonic functions defined by a linear operator. General Mathematics Notes, 13(1), 10–20.

This work is licensed under a Creative Commons Attribution 4.0 International License.
.jpg)

