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http://dx.doi.org/10.5666/KMJ.2018.58.2.243

Certain Subclasses of k-uniformly Functions Involving the Generalized Fractional Differintegral Operator  

Seoudy, Tamer Mohamed (Department of Mathematics, Faculty of Science, Fayoum University)
Publication Information
Kyungpook Mathematical Journal / v.58, no.2, 2018 , pp. 243-255 More about this Journal
Abstract
We introduce several k-uniformly subclasses of p-valent functions defined by the generalized fractional differintegral operator and investigate various inclusion relationships for these subclasses. Some interesting applications involving certain classes of integral operators are also considered.
Keywords
analytic functions; k-uniformly starlike functions; k-uniformly convex functions; k-uniformly close-to-convex functions; k-uniformly quasi-convex functions; integral operator; Hadamard product; subordination;
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1 J. K. Prajapat, R. K. Raina and H. M. Srivastava, Some inclusion properties for certain subclasses of strongly starlike and strongly convex functions involving a family of fractional integral operators, Integral Transforms Spec. Funct., 18(9)(2007), 639-651.   DOI
2 F. Ronning, A survey on uniformly convex and uniformly starlike functions, Ann. Univ. Mariae Curie-Sklodowska, 47(13)(1993), 123-134.
3 H. M. Srivastava and M. K. Aouf, A certain fractional derivative operator and its applications to a new class of analytic and multivalent functions with negative coefficients I and II, J. Math. Anal. Appl., 171(1992), 1-13   DOI
4 H. M. Srivastava and M. K. Aouf, A certain fractional derivative operator and its applications to a new class of analytic and multivalent functions with negative coefficients I and II, J. Math. Anal. Appl., 192(1995), 673-688.   DOI
5 H. M. Srivastava and S. Owa, Some characterization and distortion theorems involving fractional calculus, generalized hypergeometric functions, Hadamard products, linear operators, and certain subclasses of analytic functions, Nagoya Math. J., 106(1987), 1-28.   DOI
6 H. M. Srivastava, M. Saigo and S. Owa, A class of distortion theorems involving certain operators of fractional calculus, J. Math. Anal. Appl., 131(1988), 412-420.   DOI
7 H. Tang, G.-T. Deng, S.-H. Li and M. K. Aouf, Inclusion results for certain subclasses of spiral-like multivalent functions involving a generalized fractional differintegral operator, Integral Transforms Spec. Funct., 24(11)(2013), 873-883.   DOI
8 P. Eenigenburg, S. S. Miller, P. T. Mocanu and M. O. Reade, On a Briot-Bouquet differential subordination, General Inequalities, Birkhauser, Basel, Switzerland, 3(1983), 339-348.
9 A. W. Goodman, On uniformly starlike functions, J. Math. Anal. Appl.. 155(1991), 364-370.   DOI
10 G. P. Goyal and J. K. Prajapat, A new class of analytic p-valent functions with negative coefficients and fractional calculus operators, Tamsui Oxf. J. Math. Sci., 20(2)(2004), 175-186.
11 S. S. Miller and P. T. Mocanu, Differential subordinations and univalent functions, Michigan Math. J., 28(2)(1981), 157-172.   DOI
12 S. S. Miller and P. T. Mocanu, Differential subordinations: theory and applications, Monographs and Textbooks in Pure and Applied Mathematics 225, Marcel Dekker, New York and Basel, 2000.
13 K. I. Noor, On quasiconvex functions and related topics, Internat. J. Math. Math. Sci., 10(1987), 241-258.   DOI
14 S. Owa, On the distortion theorems I, Kyungpook Math. J., 18(1978), 53-59.
15 S. Owa, On certain classes of p-valent functions with negative coefficients, Simon Stevin, 59(4)(1985), 385-402.
16 J. K. Prajapat, Inclusion properties for certain classes of analytic functions involving a family of fractional integral operators, Fract. Calc. Appl. Anal., 11(1)(2008), 27-34.
17 S. Owa and H. M. Srivastava, Univalent and starlike generalized hypergeometric functions, Canad. J. Math., 39(1987), 1057-1077.   DOI
18 J. Patel and A. K. Mishra, On certain subclasses of multivalent functions associated with an extended fractional differintegral operator, J. Math. Anal. Appl., 332(2007), 109-122.   DOI
19 D. A. Patil and N. K. Thakare, On convex hulls and extreme points of p-valent starlike and convex classes with applications, Bull. Math. Soc. Sci. Math. R. S. Roumanie (N.S), 27(1983), 145-160.
20 J. K. Prajapat and M. K. Aouf, Majorization problem for certain class of p-valently analytic function defined by generalized fractional differintegral operator, Comput. Math. Appl., 63(1)(2012), 42-47.   DOI
21 J. H. Choi, M. Saigo and H. M. Srivastava, Some inclusion properties of a certain family of integral operators, J. Math. Anal. Appl., 276(2002), 432-445.   DOI
22 J. K. Prajapat and R. K. Raina, New sufficient conditions for starlikeness of analytic functions involving a fractional differintegral operator, Demonstratio Math., 43(4)(2010), 805-813.
23 H. A. Al-Kharsani, Multiplier transformations and k-uniformly p-valent starlike functions, Gen. Math., 17(1)(2009), 13-22.
24 M. K. Aouf, On a class of p-valent close-to-convex functions of order ${\beta}$ and type ${\alpha}$, Internat. J. Math. Math. Sci., 11(2)(1988), 259-266.   DOI
25 N. E. Cho, O. S. Kwon and H. M. Srivastava, Inclusion relationships and argument properties for certain subclasses of multivalent functions associated with a family of linear operators, J. Math. Anal. Appl., 292(2004), 470-483.   DOI