Abstract
Within this manuscript, we introduce an innovative subclass of multivalent harmonic functions, encompassing higher-order derivatives within the confines of an open unit disk. Our investigation extends to the analysis of coefficient bounds, growth estimates, starlikeness, and convexity radii uniquely associated with this particular class. Furthermore, we scrutinize the property of closure under convolution operations for this subclass.
Keywords
harmonic multivalent functions coefficient bounds distortion theorem starlikeness radii convexity radii convolution
References
- [1] O.P. Ahuja and J.M. Jahangiri, Multivalent harmonic starlike functions with missing coefficients, Math. Sci. Res. J. 7, 347-352, 2003.
- [2] O.P. Ahuja and J.M. Jahangiri, Multivalent harmonic convex functions, Math. Sci. Res. J. 11 (9), 537, 2007.
- [3] O. Al-Refai, Some properties for a class of analytic functions defined by a higher-order differential inequality, Turk. J. Math. 43 (5), 2473-2493, 2019.
- [4] J. Clunie and T. Sheil-Small, Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser. A I Math. 9, 3-25, 1984.
- [5] S. Çakmak, E. Yasar, and S. Yalçn, New subclass of the class of close-to-convex harmonic mappings defined by a third-order differential inequality, Hacet. J. Math. Stat. 51 (1), 172-186, 2022.
- [6] M. Dorff, Convolutions of planar harmonic convex mappings, Complex Var. Elliptic Equ. 45 (3), 263-271, 2001.
- [7] P.L. Duren, Univalent Functions, in: Grundlehren Der Mathematischen Wissenschaften, vol. 259, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1983.
- [8] L. Fejér, Über die Positivität von Summen, Acta Sci. Szeged, 75-86, 1925.
- [9] M.R. Goodloe, Hadamard products of convex harmonic mappings, Complex Var. Theory Appl. 47 (2), 81-92, 2004.
- [10] G.I. Oros, S. Yalçn, and H. Bayram, Some Properties of Certain Multivalent Harmonic Functions, Mathematics 11 (11), 2416, 2023.
- [11] S. Owa, T. Hayami, K. Kuroki, Some properties of certain analytic functions, Int. J. Math. Math. Sci. 2007, Hindawi.
- [12] M. A. Rosihan, S.K. Lee, K.G. Subramanian, A. Swaminathan, A third-order differential equation and starlikeness of a double integral operator, Abstr. Appl. Anal. 2011.
- [13] R. Singh and S. Singh, Convolution properties of a class of starlike functions, Proc. Am. Math. Soc. 106 (1), 145-152, 1989.
- [14] E. Yasar and S.Y. Tokgöz, Close-to-convexity of a class of harmonic mappings defined by a third-order differential inequality, Turk. J. Math. 45 (2), 678-694, 2021.
Abstract
References
- [1] O.P. Ahuja and J.M. Jahangiri, Multivalent harmonic starlike functions with missing coefficients, Math. Sci. Res. J. 7, 347-352, 2003.
- [2] O.P. Ahuja and J.M. Jahangiri, Multivalent harmonic convex functions, Math. Sci. Res. J. 11 (9), 537, 2007.
- [3] O. Al-Refai, Some properties for a class of analytic functions defined by a higher-order differential inequality, Turk. J. Math. 43 (5), 2473-2493, 2019.
- [4] J. Clunie and T. Sheil-Small, Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser. A I Math. 9, 3-25, 1984.
- [5] S. Çakmak, E. Yasar, and S. Yalçn, New subclass of the class of close-to-convex harmonic mappings defined by a third-order differential inequality, Hacet. J. Math. Stat. 51 (1), 172-186, 2022.
- [6] M. Dorff, Convolutions of planar harmonic convex mappings, Complex Var. Elliptic Equ. 45 (3), 263-271, 2001.
- [7] P.L. Duren, Univalent Functions, in: Grundlehren Der Mathematischen Wissenschaften, vol. 259, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1983.
- [8] L. Fejér, Über die Positivität von Summen, Acta Sci. Szeged, 75-86, 1925.
- [9] M.R. Goodloe, Hadamard products of convex harmonic mappings, Complex Var. Theory Appl. 47 (2), 81-92, 2004.
- [10] G.I. Oros, S. Yalçn, and H. Bayram, Some Properties of Certain Multivalent Harmonic Functions, Mathematics 11 (11), 2416, 2023.
- [11] S. Owa, T. Hayami, K. Kuroki, Some properties of certain analytic functions, Int. J. Math. Math. Sci. 2007, Hindawi.
- [12] M. A. Rosihan, S.K. Lee, K.G. Subramanian, A. Swaminathan, A third-order differential equation and starlikeness of a double integral operator, Abstr. Appl. Anal. 2011.
- [13] R. Singh and S. Singh, Convolution properties of a class of starlike functions, Proc. Am. Math. Soc. 106 (1), 145-152, 1989.
- [14] E. Yasar and S.Y. Tokgöz, Close-to-convexity of a class of harmonic mappings defined by a third-order differential inequality, Turk. J. Math. 45 (2), 678-694, 2021.
Details
| Primary Language | English |
|---|---|
| Subjects | Real and Complex Functions (Incl. Several Variables) |
| Journal Section | Mathematics |
| Authors | |
| Early Pub Date | August 27, 2024 |
| Publication Date | April 28, 2025 |
| Submission Date | January 30, 2024 |
| Acceptance Date | June 9, 2024 |
| Published in Issue | Year 2025 Volume: 54 Issue: 2 |