Certain Sub-Classes of Harmonic Univalent Functions Associated With the Differential Operator
DOI:
https://doi.org/10.29304/jqcsm.2025.17.22223Keywords:
Harmonic Functions, univalent Functions, Sense-Preserving, extreme Points, distortion TheoremAbstract
In the present study, a subclass of harmonic univalent functions defined by a differential operator acting on complex harmonic functions is tackled. A sufficient condition and a representation theorem for the subclass are derived. Some geometric properties associated with it are also investigated, including coefficient bound, extreme points, distortion and convex combinations in connection to the subclass
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References
J. Clunie and T. Sheil-Small, "Harmonic univalent functions," Annales Academiae Scientiarum Fennicae Mathematica, vol. 9, pp. 3-25, 1984.
P. Duren, "Harmonic mappings in the plane," Cambridge University Press, Cambridge, United Kingdom, 2004.
O. P. Ahuja, "Planar harmonic univalent and related mappings," Journal of Inequalities in Pure and Applied Mathematics, vol. 6, no. 4, pp. 1-18, 2005.
J. M. Jahangiri, G. Murugusundaramoorthy, and K. Vijaya, "Salagean-type harmonic univalent functions," South J. Pure Appl. Math., vol. 2, no. 6, pp. 77-82, 2002.
A. R. S. Juma and L. I. Cotˆırla, "On harmonic univalent function defined by generalized Salagean derivatives," Acta Universitatis Apulensis, vol. 23, pp. 179-188, 2010.
Z. S. Ghali and A. K. Wanas, "Some Characteristics Properties for Linear Operator on Class of Multivalent Analytic Functions Defined by Differential Subordination," Journal of Al-Qadisiyah for Computer Science and Mathematics, vol. 16, no. 3, pp. 36-43, 2024.
Q. A. Shakir, F. M. Sakar, "On Third-Order Differential Subordination and Superordination Properties of Analytic Functions Defined by Tayyah-Atshan Fractional Integral Operator" Advances in Nonlinear Variational Inequalities. (2025). https://doi.org/10.52783/anvi.v28.2528.
A. M. Rashid and A. R. S. Juma, "A class of harmonic univalent functions defined by the q-derivative operator," International Journal of Nonlinear Analysis and Applications, vol. 13, no. 1, pp. 2713-2722, 2022.
N. E. Cho and T. H. Kim, "Multiplier transformations and strongly close-to-convex functions," Bulletin of the Korean Mathematical Society, vol. 40, no. 3, pp. 399-410, 2003.
J. M. Jahangiri, "Harmonic functions starlike in the unit disk," Journal of Mathematical Analysis and Applications, vol. 235, no. 2, pp. 470-477, 1999.
G. S. Salagean, "Subclasses of univalent functions," in Complex Analysis – Fifth Romanian-Finnish Seminar. Lecture Notes in Mathematics, pp. 362-372. Springer, Berlin, Heidelberg, 1983.
H. Bayram and S. Yalçın, "A subclass of harmonic univalent functions defined by a linear operator," Palestine Journal of Mathematics, vol. 6, Special Issue: II, pp. 320-326, 2017.
B. A. Uralegaddi and C. Somanatha, "Certain classes of univalent functions," in Current Topics in Analytic Function Theory, pp. 371-374, 1992.
S. Yalçın, G. Murugusundaramoorthy, and K. Vijaya, "Inclusion results on subclasses of harmonic univalent functions associated with Pascal distribution series," Palestine J. Math, vol. 11, pp. 267-275, 2022.
T. Rosy, B. A. Stephen, K. G. Subramanian, and J. M. Jahangiri, "Goodman-Ronning-type harmonic univalent functions," Kyungpook Mathematical Journal, vol. 41, no. 1, pp. 45, 2001.
Y. Avci, "On harmonic univalent mappings," Ann. Univ. Marie Curie-Sklodowska Sect. A, vol. 44, pp. 1-7, 1991.
H. Silverman and E. M. Silvia, "Subclasses of harmonic univalent functions," New Zealand Journal of Mathematics, vol. 28, pp. 275-284, 1999.
H. Silverman, "Harmonic univalent functions with negative coefficients," Journal of Mathematical Analysis and Applications, vol. 220, no. 1, pp. 283-289, 1998.
J. M. Jahangiri, "Harmonic functions starlike in the unit disk," Journal of Mathematical Analysis and Applications, vol. 235, no. 2, pp. 470-477, 1999.
E. Yasar and S. Yalçin, "Certain properties of a subclass of harmonic functions," Applied Mathematics & Information Sciences, vol. 7, no. 5, pp. 1749-1753, 2013.
S. Yalçin, M. Öztürk, and M. Yamankaradeniz, "On the subclass of Salagean-type harmonic univalent functions," J. Inequal. Pure Appl. Math, vol. 8, no. 2, pp. 1-9, 2007.
R. Kumar, S. Gupta, and S. U. K. H. J. I. T. Singh, "A class of univalent harmonic functions defined by multiplier transformation," Rev. Roumaine Math. Pures Appl, vol. 57, no. 1, pp. 371-382, 2012.
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