Geometric properties and neighborhood results for a subclass of analytic functions involving Komatu integral
DOI:
https://doi.org/10.24193/subbmath.2017.3.10Keywords:
Analytic function, Komatu integral, coefficient inequality, Fekete- Szegö inequality, extreme points, radii of starlikeness and convexity, neighbor- hood results.Abstract
In this paper, a subclass of analytic function is defined using Komatu integral. Coefficient inequalities, Fekete-Szegö inequality, extreme points, radii of starlikeness and convexity and integral means inequality for this class are obtained. Distortion theorem for the generalized fractional integration introduced by Saigo are also obtained. The inclusion relations associated with the (n,µ)- neighborhood also have been found for this class.
Mathematics Subject Classification (2010): 47A15, 46A32, 47D20.
References
Agarwal, R., Paliwal, G.S., On the Fekete-Szego problem for certain subclasses of analytic function, Proceedings of the Second International Conference on Soft Computing for Problem Solving (SocProS 2012), December 28-30, 2012, Advances in Intelligent Systems and Computing, 236(2014), 353-361.
Atshan, W.G., Fractional Calculus on a Subclass of Spiral-Like Functions Defined by Komatu Operator, International Mathematical Forum, 3(32)(2008), 1587-1594.
Bansal, D., Fekete-Szeg¨o problem for a new class of analytic function, International Journal of Mathematics and Mathematical Science, 2011, article ID 143096, 5 pp.
Komatu, Y., On analytic prolongation of a family of integral operators, Mathematica (Cluj), 32(55)(1990), 141-145.
Li, J.L., On some classes of analytic functions, Mathematica Japonica, 40(3)(1994), 523-529.
Libera, R.J., Zlotkiewicz, E.J., Coefficient bounds for the inverse of a function with derivative in ρ, Proc. Amer. Math. Soc., 87(2)(1983), 251-257.
Littlewood, J.E., On inequalities in theory of functions, Proc. London Math. Soc., 23(1925), 481-519.
Ma, W., Minda, D., A unified treatment of some special classes of univalent functions, in: Proceedings of the Conference on Complex Analysis (Li, Z., Ren, F., Yang, L. and Zhang, S. eds.) Conference Proceeding and Lecture Notes in Analysis, International Press, Cambridge, Massachusetts, 1(1994), 157-169.
Murugusundaramoorthy, G., Srivastava, H.M., Neighborhood of certain classes of analytic functions of complex order, Journal of Inequalities in Pure and Applied Mathemat- ics, 5(2)(2004), art. 24.
Ponnusamy, S., Neighborhoods and Carath´eodory functions, J. Anal., 4(1996), 41-51. [11] Ponnusamy, S., Ronning, F., Integral transforms of a class of analytic functions, Complex Var. Elliptic Equ., 53(5)(2008), 423-434.
Rusheweyh, St., Convolution in Geometric Function Theory, Les Presses de l’Univ. de Montreal, 1982.
Rusheweyh, St., Stankiewicz, J., Subordination under convex univalent function, Bull. Pol. Acad. Sci. Math., 33(1985), 499-502.
Saigo, M., A remark on integral operators involving the Gauss hypergeometric functions, Math. Rep. College General Ed. Kyushu Univ., 11(1978), 135-143.
Silverman, H., Univalent functions with negative coefficients, Proc. Amer. Math. Soc., 51(1975), 109-116.
Silverman, H., A survey with open problems on univalent functions whose coefficients are negative, Rocky Mountain J. Math., 21(1991), 1099-1125.
Silverman, H., Integral means for univalent functions with negative coefficients, Houston J. Math., 23(1997), 169-174.
Sokol, J., On sufficient condition for starlikeness of certain integral of analytic function, J. Math. Appl., 28(2006), 127-130.
Srivastava, H.M., Saigo, M., Owa, S., A class of distortion theorems involving certain operators of fractional calculus of starlike functions, J. Math. Anal. Appl., 131(1988), 412-420.
Swaminathan, A., Sufficient conditions for hypergeometric functions to be in a certain class of analytic functions, Computers and Mathematics with Applications, 59(4)(2010), 1578-1583.
Vijaya, K., Deepa, K., Neighborhood and partial sums results on the class of starlike functions involving Dziok-Srivastava operator, Stud. Univ. Babe¸s-Bolyai Math., 58(2)(2013), 171180.
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