Applications of Fractional Calculus on a Certain Class of Univalent Functions Associated with Wanas Operator
Abstract
The purpose of this work is to use fractional integral and Wanas operator to define a certain class of analytic and univalent functions defined in the open unit disk U. Also, we obtain some results for this class such as integral representation, inclusion relationship and argument estimate.
References
J. W. Alexander, Functions which map the interior of the unit circle upon simple region, Annals of Mathematics 17(1) (1915), 12-22. https://doi.org/10.2307/2007212
F. M. Al-Oboudi, On univalent functions defined by a generalized Salagean operator, Int. J. Math. Math. Sci. 27 (2004), 1429-1436. https://doi.org/10.1155/S0161171204108090
N. E. Cho and M. K. Aouf, Some applications of fractional calculus operators to a certain subclass of analytic functions with negative coefficients, Turkish J. Math. 20 (1996), 553 562.
S. D. Bernardi, Convex and starlike univalent functions, Trans. Amer. Math. Soc. 135 (1969), 429-446. https://doi.org/10.1090/S0002-9947-1969-0232920-2
N. E. Cho and H. M. Srivastava, Argument estimates of certain analytic functions defined by a class of multiplier transformations, Math. Comput. Modeling 37(1-2) (2003), 39-49. https://doi.org/10.1016/S0895-7177(03)80004-3
N. E. Cho and T. H. Kim, Multiplier transformations and strongly close-to-convex functions, Bull. Korean Math. Soc. 40(3) (2003), 399-410. https://doi.org/10.4134/BKMS.2003.40.3.399
A. Ebadian, S. Shams, Z. G. Wang and Y. Sun, A class of multivalent analytic functions involving the generalized Jung-Kim-Srivastava operator, Acta Univ. Apulensis 18 (2009), 265-277.
P. J. Eenigenburg, S. S. Miller, P. T. Mocanu and M. O. Reade, On a Briot-Bouquet differential subordination, General Inequalities, 3, Birkhauser, Basel, 1983, pp. 339-348. https://doi.org/10.1007/978-3-0348-6290-5_26
I. B. Jung, Y. C. Kim and H. M. Srivastava, The Hardy space of analytic functions associated with certain one-parameter families of integral operators, J. Math. Anal. Appl. 176 (1993), 138-147. https://doi.org/10.1006/jmaa.1993.1204
S. S. Miller and P. T. Mocanu, Differential subordinations and univalent functions, Michigan Math. J. 28 (1981), 157-171. https://doi.org/10.1307/mmj/1029002507
G. S. Salagean, Subclasses of univalent functions, Lecture Notes in Math., 1013, Springer Verlag, Berlin, 1983, pp. 362-372. https://doi.org/10.1007/BFb0066543
H. Silverman and E. M. Silvia, Subclasses of starlike functions subordinate to convex functions, Canad. J. Math. 37 (1985), 48-61. https://doi.org/10.4153/CJM-1985-004-7
H. M. Srivastava and A. A. Attiya, An integral operator associated with the Hurwitz-Lerch Zeta function and differential subordination, Integral Transforms Spec. Funct. 18(3) (2007), 207-216. https://doi.org/10.1080/10652460701208577
S. R. Swamy, Inclusion properties of certain subclasses of analytic functions, Int. Math. Forum 7(36) (2012), 1751-1760.
B. A. Uralegaddi and C. Somanatha, Certain classes of univalent functions, Current Topics in Analytic Function Theory, (Edited by H. M. Srivastava and S. Own), 371-374, World Scientific, Singapore, 1992. https://doi.org/10.1142/9789814355896_0032
A. K. Wanas, New differential operator for holomorphic functions, Earthline J. Math. Sci. 2(2) (2019), 527-537. https://doi.org/10.34198/ejms.2219.527537
A. K. Wanas, Some subordination results for fractional integral involving Wanas differential operator, Earthline J. Math. Sci. 3(2) (2020), 199-205. https://doi.org/10.34198/ejms.3220.199205
A. K. Wanas and G. Murugusundaramoorthy, Differential sandwich results for Wanas operator of analytic functions, Math. Morav. 24(1) (2020), 17-28. https://doi.org/10.5937/MatMor2001017K
This work is licensed under a Creative Commons Attribution 4.0 International License.