On (p,q)-Starlike Harmonic Functions Defined By Subordination
Keywords:
Complex harmonic functions univalent functions (p,q)-calculus
Abstract
We introduce and investigate classes of (p,q)-starlike harmonic univalent functions defined by subordination. We first obtained a coefficient characterization of these functions. We give necessary and sufficient convolution conditions, distortion bounds, compactness and extreme points for the (p,q)-starlike harmonic univalent with negative coefficients.
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References
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[19] S. Yalçın and H. Bayram, “Some Properties On q-Starlike Harmonic Functions Defined By Subordination”, Applied Analysis and Optimization, 4(3) (2020), 299-308.
[20] A. E. Hadi, and W. G. Atshan. “Strong Subordination for P-Valent Functions Involving A Linear Operator.” Journal of Physics: Conference Series. Vol. 1818. No. 1. IOP Publishing, 2021.
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[22] W. G. Atshan, A. H. Battor, and A. F. Abaas. “On Third-Order Differential Subordination Results for Univalent Analytic Functions Involving An Operator.” Journal of Physics: Conference Series. Vol. 1664. No. 1. IOP Publishing, 2020.
[23] W. G. Atshan, A. H. Battor, and A. F. Abaas. “Some sandwich theorems for meromorphic univalent functions defined by new integral operator.” Journal of Interdisciplinary Mathematics (2021): 1-13.
[24] A.-A. Sarah, W. G. Atshan, and F. A. AL-Maamori. “On sandwich results of univalent functions defined by a linear operator.” Journal of Interdisciplinary Mathematics 23.4 (2020): 803-809.
[25] W. G. Atshan, and N. A. Jiben. “Differential subordination and superordination for multivalent functions involving a generalized differential operator.” International Journal of Advanced Research in Science, Engineering and Technology 4.10 (2017): 4767-4775.
[2] O. P. Ahuja, A. Çetinkaya, Y. Polatoglu, “Harmonic Univalent Convex Functions Using A Quantum Calculus Approach”, Acta Universitatis Apulensis, 58, 67-81 (2019).
[3] Om P. Ahuja, A. Çetinkaya, Y. Polatoglu, “Bieberbach-de Branges and Fekete-Szegö inequalities for certain families of q-convex and q-close-to-convex functions,” J. Comput. Anal. Appl. 26(4) (2019), 639-649.
[4] R. Chakrabarti and R. Jagannathan, “A (p, q)-oscillator realization of two-parameter quantum algebras”, J. Phys. A 24(13) (1991), L711.L718.
[5] J. Clunie and T. Sheil-Small, “Harmonic univalent functions”, Ann. Acad. Sci. Fenn. Ser. A I Math. 9, 3-25 (1984).
[6] J. Dziok, “Classes of harmonic functions de.ned by subordination”, Abstr. Appl. Anal. 2015, Article ID 756928 (2015).
[7] J. Dziok, “On Janowski harmonic functions”, J. Appl. Anal. 21, 99-107 (2015).
[8] J. Dziok, “Classes of harmonic functions associated with Ruscheweyh derivatives,” Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemática 113(2) 1315.1329 (2019).
[9] J. Dziok, J. M. Jahangiri and H. Silverman, Harmonic functions with varying coefficients, Journal of Inequalities and Applications, 139, (2016).
[10] J. Dziok, S. Yalçın and S. Altınkaya, “Subclasses Of Harmonic Univalent Functions Associated With Generalized Ruscheweyh Operator”, Publications De L.institut Mathématique, Nouvelle série, tome 106 (120) 19.28, (2019).
[11] M. E. H. Ismail, E. Merkes, D. Steyr, “A generalization of starlike functions”, Complex Variables Theory Appl. 14(1) (1990), 77-84.
[12] F. H. Jackson, “On q-functions and a certain di¤erence operator”, Transactions of the Royal Society of Edinburgh, Vol:46 (1908), 253-281.
[13] J. M. Jahangiri, “Harmonic functions starlike in the unit disk”, J. Math. Anal. Appl. 235, 470-477 (1999).
[14] J. M. Jahangiri, “Harmonic Univalent Functions De.ned By q-Calculus Operators”, International Journal of Mathematical Analysis and Applications, 5(2) 39-43, (2018).
[15] V. Sahai and S. Yadav, “Representations of two parameter quantum algebras and p, q-special functions”, J. Math. Anal. Appl. 335 (2007), 268.279.
[16] T. M. Seoudy, M. K. Aouf, “Coefficient estimates of new classes of q-starlike and q-convex functions of complex order”, J. Math. Inequal. 10(1) (2016), 135-145.
[17] H. Silverman, “Harmonic univalent functions with negative coefficients”, J.Math. Anal. Appl. 220, 283-289 (1998).
[18] H. Silverman and E. M. Silvia, “Subclasses of harmonic univalent functions”, N. Z. J. Math. 28, 275-284 (1999).
[19] S. Yalçın and H. Bayram, “Some Properties On q-Starlike Harmonic Functions Defined By Subordination”, Applied Analysis and Optimization, 4(3) (2020), 299-308.
[20] A. E. Hadi, and W. G. Atshan. “Strong Subordination for P-Valent Functions Involving A Linear Operator.” Journal of Physics: Conference Series. Vol. 1818. No. 1. IOP Publishing, 2021.
[21] W. G. Atshan, and A. H. Rasha. “Some Differential Subordination and Superordination Results of p-valent Functions Defined by Differential Operator.” Journal of Physics: Conference Series. Vol. 1664. No. 1. IOP Publishing, 2020.
[22] W. G. Atshan, A. H. Battor, and A. F. Abaas. “On Third-Order Differential Subordination Results for Univalent Analytic Functions Involving An Operator.” Journal of Physics: Conference Series. Vol. 1664. No. 1. IOP Publishing, 2020.
[23] W. G. Atshan, A. H. Battor, and A. F. Abaas. “Some sandwich theorems for meromorphic univalent functions defined by new integral operator.” Journal of Interdisciplinary Mathematics (2021): 1-13.
[24] A.-A. Sarah, W. G. Atshan, and F. A. AL-Maamori. “On sandwich results of univalent functions defined by a linear operator.” Journal of Interdisciplinary Mathematics 23.4 (2020): 803-809.
[25] W. G. Atshan, and N. A. Jiben. “Differential subordination and superordination for multivalent functions involving a generalized differential operator.” International Journal of Advanced Research in Science, Engineering and Technology 4.10 (2017): 4767-4775.
Published
2021-08-25
How to Cite
BAYRAM, H., & Sibel Yalçın. (2021). On (p,q)-Starlike Harmonic Functions Defined By Subordination. Al-Qadisiyah Journal of Pure Science, 26(4), 491-500. https://doi.org/10.29350/qjps.2021.26.3.1364
Section
Special Issue (Silver Jubilee)
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