q-Analogue of New Subclass of Salagean-type Harmonic Univalent Functions defined by Subordination
Abstract
We introduce and investigate q-analogue of a new subclass of Salagean-type 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 this subclass of harmonic univalent functions with negative coefficients.
References
O. P. Ahuja, A. Çetinkaya and Y. Polatoğlu, Harmonic univalent convex functions using a quantum calculus approach, Acta Universitatis Apulensis 58 (2019), 67-81. https://doi.org/10.17114/j.aua.2019.58.06
O. P. Ahuja and A. Çetinkaya, Connecting quantum calculus and harmonic starlike functions, Filomat 34(5) (2020), 1431-1441. https://doi.org/10.2298/FIL2005431A
Ş. Altınkaya, S. Çakmak and S. Yalçın, On a new class of Salagean-type harmonic univalent functions associated with subordination, Honam Mathematical Journal 40(3) (2018), 433-446.
A. Aral, R. Agarwal and V. Gupta, Applications of q-Calculus in Operator Theory, New York, NY: Springer, 2013. https://doi.org/10.1007/978-1-4614-6946-9
J. Clunie and T. Sheil-Small, Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser. A I Math. 9 (1984), 3-25. https://doi.org/10.5186/aasfm.1984.0905
J. Dziok, Classes of harmonic functions defined by subordination, Abstr. Appl. Anal. 2015 (2015), Article ID 756928. https://doi.org/10.1155/2015/756928
J. Dziok, On Janowski harmonic functions, J. Appl. Anal. 21 (2015), 99-107. https://doi.org/10.1515/jaa-2015-0010
J. Dziok, J. M. Jahangiri and H. Silverman, Harmonic functions with varying coefficients, Journal of Inequalities and Applications 139 (2016), 1-12. https://doi.org/10.1186/s13660-016-1079-z
J. Dziok, S. Yalçın and Ş. Altınkaya, Subclasses of harmonic univalent functions associated with generalized Ruscheweyh operator, Publications de l'Institut Mathematique 106(120) (2019), 19-28. https://doi.org/10.2298/PIM1920019D
M. E. H. Ismail, E. Merkes and D. Steyr, A generalization of starlike functions, Complex Variables Theory Appl. 14(1) (1990), 77-84. https://doi.org/10.1080/17476939008814407
F. H. Jackson, On q-functions and a certain difference operator, Transactions of the Royal Society of Edinburgh 46 (1908), 253-281. https://doi.org/10.1017/S0080456800002751
J. M. Jahangiri, Harmonic functions starlike in the unit disk, J. Math. Anal. Appl. 235 (1999), 470-477. https://doi.org/10.1006/jmaa.1999.6377
J. M. Jahangiri, Harmonic univalent functions defined by q-calculus operators, International Journal of Mathematical Analysis and Applications 5(2) (2018), 39-43.
J. M. Jahangiri, G. Murugusundaramoorthy and K. Vijaya, Salagean-type harmonic univalent functions, South J. Pure Appl. Math. 2 (2002), 77-82.
M. Öztürk and S. Yalçın, On univalent harmonic functions, J. Inequal. Pure Appl. Math. 3-4 (2002), Article 61.
G. S. Salagean, Subclasses of univalent functions, Lecture Notes in Math., 1013, Springer-Verlag Heidelberg, 1983, pp. 362-372. https://doi.org/10.1007/BFb0066543
P. Sharma and O. Mishra, A class of harmonic functions associated with a q-Salagean operator, U.P.B. Sci. Bull. Series A 82(3) (2020), 3-12.
H. Silverman and E. M. Silvia, Subclasses of harmonic univalent functions, New Zealand J. Math. 28 (1999), 275-284.
S. Yalçın and H. Bayram, Some properties on q-starlike harmonic functions defined by subordination, Appl. Anal. Optim. 4(3) (2020), 299-308.
S. Yalçın and M. Öztürk, A new subclass of complex harmonic functions, Mathematical Inequalities and Applications 7(1) (2004), 55-61. https://doi.org/10.7153/mia-07-07
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