NEW CLASSES OF HARMONIC FUNCTIONS DEFINED BY FRACTIONAL OPERATOR
In the present study, we introduce an investigation of new subclasses of harmonic functions which are dened by fractional operator. Firstly, using by fractional operator, we dene new subclasses of harmonic functions. Later, we obtain main theorems of our study which contain sucient and necessary coecient bounds for functions related to the classes newly dened. Also, several particular characterization properties of these classes are given. Some of these properties involve extreme points, convex combination, distortion bounds. Finally, several corollaries of the main theorems are presented.
___
- Ahuja, O. P. and Jahangiri, J. M., (2001), Multivalent harmonic starlike functions, Ann. Univ. Marie
- Curie-Sklodowska, Sect. A., (55), pp.1-13. Altınkaya, S¸ and Yal¸cın, S. (2016), On a class of harmonic univalent functions defined by using a new differential operator, Theory and Applications of Mathematics and Computer Science (TAMCS), (2), pp.125-133.
- Avcı, Y. and Zlotkiewicz, E., (1990), On Harmonic Univalent Mappings, Ann. Unv. Mariae Cruie Sklodowska Sect. A., 44, pp.1-7.
- Aydo˘gan, M., Kahramaner, Y. and Polato˘glu, Y., (2013), Close-to-Convex Functions Defined by
- Fractional Operator, Applied Mathematical Sciences, 7(56), pp.2769-2775.
- Clunie, J. and Sheil-Small, T., (1984), Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser. A. I. Math., 9(3), pp.3-25.
- Jahangiri, J. M., (1999), Harmonic functions starlike in the unit disk,J. Math. Anal. Appl., 235, pp.470-477.
- Jahangiri, J. M., Kim, Y. C. and Srivastava, H. M.,(2003),Construction of a certain class of harmonic close-to-convex functions associated with Alexander integral transform, Integral Trans Spec Funct., , pp.237-242.
- Kilbas, A. A., Srivastava, H. M. and Trujilo, J. J., (2006), Theory Applications of Fractional Differ- ential Equations, Elsevier Publ., North- Holland Mathematics Studies, 204.
- Miller, K. S. and Ross, B., (1993), An Introduction to the Fractional Calculus and Fractional Differ- ential Equations, John Wiley and Sond Inc., New York.
- Oldham, K. B. and Spanier, J., (1974), The Fractional Calculus, Academic Press.
- Silverman, H.,(1998), Harmonic univalent functions with negative coefficients, J. Math. Anal. Appl., , pp.283-289.
- Srivastava, H. M. and Owa, S., (1989), Univalent Functions, Fractional Calculus and Their Applica- tions, Jhon Wiley and Sons, New York.
- Silverman, H. and Silvia, E. M. (1999), Subclasses of harmonic univalent functions, New Zealand J. Math., 28, pp.275-284.
- Yal¸cın, S., Joshi, S. B. and Ya¸sar, E. (2010), On Certain Subclass of Harmonic Univalent Functions Defined by a Generalized Ruscheweyh Derivatives Operator, Applied Mathematical Sciences, 4(7), pp.327-336.
- ISSN: 2146-1147
- Başlangıç: 2010
- Yayıncı: Turkic World Mathematical Society
Sayıdaki Diğer Makaleler
F.m. SAKAR, Y. BAGCI, H. Ö. GÜNEY
D.l. SUTHAR, S.d. PUROHİT, K.s. NİSAR