Close-to-convexity of a class of harmonic mappings defined by a third-order differential inequality

YAŞAR, Elif; Yalçın, Sibel

doi:10.3906/mat-2004-50

Close-to-convexity of a class of harmonic mappings defined by a third-order differential inequality

Elif YAŞAR, (Bursa Uludağ Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Bursa, Türkiye)

Sibel YALÇIN (Bursa Uludağ Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Bursa, Türkiye)

Turkish Journal of Mathematics

2 0

Yıl: 2021 Cilt: 45 Sayı: 2 Sayfa Aralığı: 678 - 694 Metin Dili: İngilizce DOI: 10.3906/mat-2004-50 İndeks Tarihi: 22-09-2021

Close-to-convexity of a class of harmonic mappings defined by a third-order differential inequality

Öz:

In this paper, we consider a class of normalized harmonic functions in the unit disk satisfying a third-orderdifferential inequality and we investigate several properties of this class such as close-to-convexity, coefficient bounds,growth estimates, sufficient coefficient condition, and convolution. Moreover, as an application, we construct harmonicpolynomials involving Gaussian hypergeometric function which belong to the considered class. We also provide examplesillustrating graphically with the help of Maple.

Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[1] Clunie J, Sheil-Small T. Harmonic univalent functions. Annales Academiae Scientiarum Fennicae Series A I Mathematica 1984; 9: 3-25.
[2] Dorff M. Convolutions of planar harmonic convex mappings. Complex Variables Theory and Applications 2001; 45 (3): 263-271.
[3] Duren P. Harmonic mappings in the plane. Cambridge Tracts in Mathematics. 156 Cambridge, UK: Cambridge Univ. Press, 2004.
[4] Fejér, L. Über die positivitat von summen, die nach trigonometrischen order Legendreschen funktionen fortschreiten. Acta Litt. Ac Sei. Szeged 1925; 75-86 (in German).
[5] Ghosh N, Vasudevarao A. On a subclass of harmonic close-to-convex mappings. Monatshefte für Mathematik 2019; 188: 247-267.
[6] Goodloe M. Hadamard products of convex harmonic mappings. Complex Variables Theory and Applications 2002; 47 (2): 81-92.
[7] Miller SS, Mocanu PT. Differential subordinations and univalent functions. Michigan Mathematical Journal 1981; 28: 157-171.
[8] Miller, SS, Mocanu PT. Differential Subordinations, Theory and Applications. New York, NY, USA: Marcel Dekker, 1999.
[9] Nagpal S, Ravichandran V. A subclass of close-to-convex harmonic mappings. Complex variables and Elliptic Equations 2014; 59 2: 204-216.
[10] Nagpal S, Ravichandran V. Construction of subclasses of univalent harmonic mappings. Journal of The Korean Mathematical Society 2014; 53: 567-592.
[11] Kim YC, Ponnusamy, S. Sufficiency for Gaussian hypergeometric functions to be uniformly convex. International Journal of Mathematics and Mathematical Sciences 1999; 22 (4): 765-773.
[12] Li L, Ponnusamy S. Disk of convexity of sections of univalent harmonic functions. Journal of Mathematical Analysis and Applications 2013; 408: 589-596.
[13] Li L, Ponnusamy S. Injectivity of sections of univalent harmonic mappings. Nonlinear Analysis 2013; 89 276-283.
[14] Ponnusamy S, Kaliraj AS, Starkov VV. Absolutely convex, uniformly starlike and uniformly convex harmonic mappings. Complex Variables and Elliptic Equations 2016; 61 10: 1418-1433.
[15] Ponnusamy S, Yamamoto H, Yanagihara H. Variability regions for certain families of harmonic univalent mappings. Complex Variables and Elliptic Equations 2013; 58 (1): 23-34.
[16] Rajbala C, Prajapat JK. Certain geometric properties of close-to-convex harmonic mappings. Preprint, arXiv:1910.04441.
[17] Al-Refai O. Some properties for a class of analytic functions defined by a higher-order differential inequality. Turkish Journal of Mathematics 2019; 43: 2473-2493.
[18] Rosihan MA, Lee SK, Subramanian KG, Swaminathan A. A third-order differential equation and starlikeness of a double integral operator. Abstract and Applied Analysis 2011; Article ID 901235.
[19] Singh R, Singh S. Convolution properties of a class of starlike functions. Proceedings of American Mathematical Society 1989; 106: 145-152.
[20] Temme NM. Special Functions: An Introduction to the Classical Functions of Mathematical Physics. New York, NY, USA: Wiley, 1996.

APA	YAŞAR E, Yalçın S (2021). Close-to-convexity of a class of harmonic mappings defined by a third-order differential inequality. , 678 - 694. 10.3906/mat-2004-50
Chicago	YAŞAR Elif,Yalçın Sibel Close-to-convexity of a class of harmonic mappings defined by a third-order differential inequality. (2021): 678 - 694. 10.3906/mat-2004-50
MLA	YAŞAR Elif,Yalçın Sibel Close-to-convexity of a class of harmonic mappings defined by a third-order differential inequality. , 2021, ss.678 - 694. 10.3906/mat-2004-50
AMA	YAŞAR E,Yalçın S Close-to-convexity of a class of harmonic mappings defined by a third-order differential inequality. . 2021; 678 - 694. 10.3906/mat-2004-50
Vancouver	YAŞAR E,Yalçın S Close-to-convexity of a class of harmonic mappings defined by a third-order differential inequality. . 2021; 678 - 694. 10.3906/mat-2004-50
IEEE	YAŞAR E,Yalçın S "Close-to-convexity of a class of harmonic mappings defined by a third-order differential inequality." , ss.678 - 694, 2021. 10.3906/mat-2004-50
ISNAD	YAŞAR, Elif - Yalçın, Sibel. "Close-to-convexity of a class of harmonic mappings defined by a third-order differential inequality". (2021), 678-694. https://doi.org/10.3906/mat-2004-50

APA	YAŞAR E, Yalçın S (2021). Close-to-convexity of a class of harmonic mappings defined by a third-order differential inequality. Turkish Journal of Mathematics, 45(2), 678 - 694. 10.3906/mat-2004-50
Chicago	YAŞAR Elif,Yalçın Sibel Close-to-convexity of a class of harmonic mappings defined by a third-order differential inequality. Turkish Journal of Mathematics 45, no.2 (2021): 678 - 694. 10.3906/mat-2004-50
MLA	YAŞAR Elif,Yalçın Sibel Close-to-convexity of a class of harmonic mappings defined by a third-order differential inequality. Turkish Journal of Mathematics, vol.45, no.2, 2021, ss.678 - 694. 10.3906/mat-2004-50
AMA	YAŞAR E,Yalçın S Close-to-convexity of a class of harmonic mappings defined by a third-order differential inequality. Turkish Journal of Mathematics. 2021; 45(2): 678 - 694. 10.3906/mat-2004-50
Vancouver	YAŞAR E,Yalçın S Close-to-convexity of a class of harmonic mappings defined by a third-order differential inequality. Turkish Journal of Mathematics. 2021; 45(2): 678 - 694. 10.3906/mat-2004-50
IEEE	YAŞAR E,Yalçın S "Close-to-convexity of a class of harmonic mappings defined by a third-order differential inequality." Turkish Journal of Mathematics, 45, ss.678 - 694, 2021. 10.3906/mat-2004-50
ISNAD	YAŞAR, Elif - Yalçın, Sibel. "Close-to-convexity of a class of harmonic mappings defined by a third-order differential inequality". Turkish Journal of Mathematics 45/2 (2021), 678-694. https://doi.org/10.3906/mat-2004-50