Abstract
The main purpose of the present paper is to investigate a number of useful properties such as sufficiency criteria, distortion bounds, coefficient estimates, radius of starlikness and radius of convexity for a new subclass of analytic functions, which are defined here by means of a newly defined q-linear differential operator.
Similar content being viewed by others
References
I. Aldawish and M. Darus, “Starlikness of q-differential operator involving quantum calculus”, Korean J. Math., 22(4), 699–709, 2014.
H. Aldweby and M. Darus, “A subclass of harmonic univalent functions associated with q-analogue of Dziok-Srivastava operator”, ISRN Math. Anal., 2013, 382312–382318, 2013.
H. Aldweby and M. Darus, “Some subordination results on q-analogue of Ruscheweyh differential operator”, Abstr. Appl. Anal., 2014, 958563–958569, 2014.
A. Aral, “On the generalized Picard and Gauss Weierstrass singular integrals”, J. Compu. Anal. Appl., 8(3), 249–261, 2006.
“A. Aral and V. Gupta, Generalized q-Baskakov operators”, Math. Slovaca, 61(4), 619–634, 2011.
A. Aral and V. Gupta, “On the Durrmeyer type modification of the q-Baskakov type operators”, Non-linear Anal. Theory, Methods and Appl., 72(3–4), 1171–1180, 2010.
A. Aral and V. Gupta, “On q-Baskakov type operators”, Demonstratio Mathematica, 42(1), 109–122, 2009.
G. A. Anastassiu and S. G. Gal, “Geometric and approximation properties of generalized singular integrals”, J. Korean Math. Soci., 23(2), 425–443, 2006.
G. A. Anastassiu and S. G. Gal, “Geometric and approximation properties of some singular integrals in the unit disk”, J. Ineq. Appl., 2006, 17231–17250, 2006.
A. Huda and M. Darus, “Integral operator defined by q-analogue of Liu-Srivastava operator”, Studia Universitatis Babes-Bolyai, Series Mathematica, 58(4), 529–537, 2013.
F. H. Jackson, “On q-definite integrals”, The Quarterly J. Pure Appl. Math., 41, 193–203, 1910.
F. H. Jackson, “On q-functions and a certain difference operator”, Trans. Royal Soc. Edinburgh, 46(2), 253–281, 1909.
S. Kanas and D. Răducanu, “Some class of analytic functions related to conic domains”, Math. Slovaca, 64(5), 1183–1196, 2014.
M. S. Liu, “On a subclass of p-valent close to convex functions of type α and order β”, J. Math. Study, 30(1), 102–104, 1997.
A. Mohammed and M. Darus, “A generalized operator involving the q-hypergeometric function”, Mat. Vesnik, 65(4), 454–465, 2013.
W. Rogosinski, “On the coefficients of subordinate functions”, Proc. London Math. Soc., 48(2), 48–82, 1943.
St. Ruscheweyh, “New criteria for univalent functions”, Proc. Amer. Math. Soc., 49, 109–115, 1975.
T. M. Seoudy and M. K. Aouf, “Coefficient estimates of new classes of q-starlike and q-convex functions of complex order”, J. Math. Inequ., 10(1), 135–145, 2016.
Author information
Authors and Affiliations
Corresponding authors
Additional information
Russian Text © The Author(s), 2019, published in Izvestiya Natsional’noi Akademii Nauk Armenii, Matematika, 2019, No. 6, pp. 19–27.
About this article
Cite this article
Arif, M., Khan, Q. & Sokół, J. A New Family of Starlike Functions in a Circular Domain Involving a q-differential Operator. J. Contemp. Mathemat. Anal. 54, 339–346 (2019). https://doi.org/10.3103/S1068362319060037
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1068362319060037