A LINEAR OPERATOR ASSOCIATED WITH THE MITTAG-LEFFLER FUNCTION AND RELATED CONFORMAL MAPPINGS

Jinlin Liu; Rekha Srivastava

doi:10.11948/2018.1886

2018 Volume 8 Issue 6

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Jinlin Liu, Rekha Srivastava. A LINEAR OPERATOR ASSOCIATED WITH THE MITTAG-LEFFLER FUNCTION AND RELATED CONFORMAL MAPPINGS[J]. Journal of Applied Analysis & Computation, 2018, 8(6): 1886-1892. doi: 10.11948/2018.1886

Citation:

Jinlin Liu, Rekha Srivastava. A LINEAR OPERATOR ASSOCIATED WITH THE MITTAG-LEFFLER FUNCTION AND RELATED CONFORMAL MAPPINGS[J]. Journal of Applied Analysis & Computation, 2018, 8(6): 1886-1892. doi: 10.11948/2018.1886

A LINEAR OPERATOR ASSOCIATED WITH THE MITTAG-LEFFLER FUNCTION AND RELATED CONFORMAL MAPPINGS

Jinlin Liu¹,
Rekha Srivastava²

1 Department of Mathematics, Yangzhou University, Yangzhou 225002, China;
2 Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada

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Abstract

Abstract

In the present paper, we introduce a linear operator associated with the Mittag-Leffler function. Some convolution properties of meromorphic functions involving this operator are given.
- Meromorphic functions /
- conformal mapping /
- Mittag-Leffler function /
- second-order differential subordination /
- Hadamard product(or convolution) /
- convex functions /
- univalent functions
MSC: 33E12;30C45

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References

[1]	A. A. Attiya, Some applications of Mittag-Leffler function in the unit disk, Filomat, 2016, 30, 2075-2081. Google Scholar
[2]	D. Bansal and J. K. Prajapat, Certain geometric properties of the MittagLeffler functions, Complex Var. Elliptic Equ., 2016, 61, 338-350. Google Scholar
[3]	M. Grag, P. Manohar and S. L. Kalla, A Mittag-Leffler-type function of two variables, Integral Transforms Spec. Funct., 2013, 24, 934-944. Google Scholar
[4]	T. H. MacGregor, Functions whose derivative has a positive real part, Trans. Amer. Math. Soc., 1962, 104, 532-537. Google Scholar
[5]	G. M. Mittag-Leffler, Sur la nouvelle fonction E(x), C. R. Acad. Sci. Paris, 1903, 137, 554-558. Google Scholar
[6]	S. Ruscheweyh, Convolutions in Geometric Function Theory, Les Presses de 1'Université,de Montréal, Montréal, 1982. Google Scholar
[7]	H. M. Srivastava, Some families of Mittag-Leffler type functions and associated operators of fractional calculus, TWMS J. Pure Appl. Math., 2016, 7, 123-145. Google Scholar
[8]	H. M. Srivastava and D. Bansal, Close-to-convexity of a certain family of qMittag-Leffler functions, J. Nonlinear Var. Anal., 2017, 1, 61-69. Google Scholar
[9]	H. M. Srivastava, B. A. Frasin and V. Pescar, Univalence of integral operators involving Mittag-Leffler functions, Appl. Math. Inform. Sci., 2017, 11, 635-641. Google Scholar
[10]	H. M. Srivastava, A. Kilicman, Z. E. Abdulnaby and R. W. Ibrahim, Generalized convolution properties based on the modified Mittag-Leffler function, J. Nonlinear Sci. Appl., 2017, 10, 4284-4294. Google Scholar
[11]	H. M. Srivastava and Ž. Tomovski, Fractional calculus with an integral operator containing a generalized Mittag-Leffler function in the kernal, Appl. Math. Comput., 2009, 211, 198-210. Google Scholar
[12]	A. Wiman, Über den Fundamental satz in der Theorie der Funcktionen E(x), Acta Math., 1905, 29, 191-201. Google Scholar