Geometric properties of an integral operator associated with Mittag-Leffler functions
DOI :
https://doi.org/10.5269/bspm.62798Résumé
The main object of this paper is to introduce a new integral operator associated with Mittag-Leffler function. Further, we obtain some sufficient condition for this integral operator belonging to certain classes of starlike functions.
Références
[1] M. Arif and M. Raza, Some properties of an integral operator defined by Bessel functions, Acta Univ. Apulensis, 26(2011), 69-74.
[2] D. Bansal and J. K. Prajapat, Certain geometric properties of the Mittag-Leffler functions, Complex Var. Elliptic Equ., 61(3) (2016), 338-350.
[3] E. Deniz, H. Orhan and H.M. Srivastava, Some sufficient conditions for univalence of certain families of integral operators involving generalized Bessel functions, Taiwanese J. Math., 15(2011), 883-917.
[4] B. A. Frasin, Sufficient condition for integral operator defined by Bessel functions, J. Math. Inequal., 4(3) (2010), 301-306.
[5] N. Magesh, S. Porwal and S.P. Singh, Some geometric properties of an integral operator involving Bessel functions, Novi Sad J. Math., 47(2) (2017), 149 - 156.
[6] S. Mahmood, H.M. Srivastava, S.N. Malik, M. Raza, N. Shahzadi and S. Zainab, A certain family of integral operators associated with the Struve functions, Symmetry, 11(2019), Art. ID 463, 1-16.
[7] G. M. Mittag-Leffler, Sur la nouvelle function E(x), C. R. Acad. Sci. Paris, 137 (1903), 554-558.
[8] S. Porwal and D. Breaz, Mapping properties of an integral operator involving Bessel functions, Analytic Number Theory, Approximation Theory and Spect. Funct., 821-826, Springer, New York, (2014).
[9] S. Porwal and M. Kumar, Mapping properties of an integral operator involving Bessel functions on some sub- classes of univalent functions, Afr. Mat., 28(1-2)(2017), 165-170
[10] S. Porwal, A. Gupta and G. Murugasundaramoorthy, New sufficient conditions for starlikeness of certain integral operators involving Bessel functions, Acta Univ. Math. Beli, series Math., (2017), 10-18.
[11] M. Raza, S. Noreen and S.N. Malik, Geometric properties of integral operators defined by Bessel functions, J. Ineq. Spec. Funct., 7(2016), 34-48.
[12] M. S. Robertson, On the theory of univalent functions, Ann. Math., 37 (1936), no. 2, 374{408.
[13] H. Silverman, Univalent functions with negative coefficients, Proc. Amer. Math. Soc., 51 (1975), 109{116.
[14] H. Shiraishi and S. Owa, Starlikeness and convexity for analytic functions concerned with Jack's Lemma, Int. J. Open Problem Comput. Math., 2(1) (2009), 37-47.
[15] H. M. Srivastava, B. A. Frasin and V. Pescar, Univalance of integral operators involving Mittag-Leffler functions, Appl. Math. Inf. Sci., 11(3) (2017), 635-641.
[16] A. Wiman, Uber den fundamental satz in der Theorie der Funcktionen E(x), Acta Math., 29(1905), 191-201.
[17] A. Wiman, Uber die Nullstellum der Funcktionen E(x), Acta Math., 29(1905), 271-234.
[2] D. Bansal and J. K. Prajapat, Certain geometric properties of the Mittag-Leffler functions, Complex Var. Elliptic Equ., 61(3) (2016), 338-350.
[3] E. Deniz, H. Orhan and H.M. Srivastava, Some sufficient conditions for univalence of certain families of integral operators involving generalized Bessel functions, Taiwanese J. Math., 15(2011), 883-917.
[4] B. A. Frasin, Sufficient condition for integral operator defined by Bessel functions, J. Math. Inequal., 4(3) (2010), 301-306.
[5] N. Magesh, S. Porwal and S.P. Singh, Some geometric properties of an integral operator involving Bessel functions, Novi Sad J. Math., 47(2) (2017), 149 - 156.
[6] S. Mahmood, H.M. Srivastava, S.N. Malik, M. Raza, N. Shahzadi and S. Zainab, A certain family of integral operators associated with the Struve functions, Symmetry, 11(2019), Art. ID 463, 1-16.
[7] G. M. Mittag-Leffler, Sur la nouvelle function E(x), C. R. Acad. Sci. Paris, 137 (1903), 554-558.
[8] S. Porwal and D. Breaz, Mapping properties of an integral operator involving Bessel functions, Analytic Number Theory, Approximation Theory and Spect. Funct., 821-826, Springer, New York, (2014).
[9] S. Porwal and M. Kumar, Mapping properties of an integral operator involving Bessel functions on some sub- classes of univalent functions, Afr. Mat., 28(1-2)(2017), 165-170
[10] S. Porwal, A. Gupta and G. Murugasundaramoorthy, New sufficient conditions for starlikeness of certain integral operators involving Bessel functions, Acta Univ. Math. Beli, series Math., (2017), 10-18.
[11] M. Raza, S. Noreen and S.N. Malik, Geometric properties of integral operators defined by Bessel functions, J. Ineq. Spec. Funct., 7(2016), 34-48.
[12] M. S. Robertson, On the theory of univalent functions, Ann. Math., 37 (1936), no. 2, 374{408.
[13] H. Silverman, Univalent functions with negative coefficients, Proc. Amer. Math. Soc., 51 (1975), 109{116.
[14] H. Shiraishi and S. Owa, Starlikeness and convexity for analytic functions concerned with Jack's Lemma, Int. J. Open Problem Comput. Math., 2(1) (2009), 37-47.
[15] H. M. Srivastava, B. A. Frasin and V. Pescar, Univalance of integral operators involving Mittag-Leffler functions, Appl. Math. Inf. Sci., 11(3) (2017), 635-641.
[16] A. Wiman, Uber den fundamental satz in der Theorie der Funcktionen E(x), Acta Math., 29(1905), 191-201.
[17] A. Wiman, Uber die Nullstellum der Funcktionen E(x), Acta Math., 29(1905), 271-234.
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2024-05-03
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Research Articles
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