Geometric properties and neighborhood results for a subclass of analytic functions involving Komatu integral

Ritu Agarwal, Gauri Shankar Paliwal, Hari Singh Parihar


In this paper, a subclass of analytic function is defined using
Komatu integral. Coefficient inequalities, Fekete-Szeg¨o inequality, extreme
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.


Analytic Function; Komatu Integral; Coefficient Inequality; FeketeSzeg¨o inequality; Extreme points; radii of Starlikeness and Convexity; Neighborhood results.

Full Text:



Agarwal, Ritu and Paliwal, G.S. (2014) On the Fekete-Szego problem for certain subclasses of analytic function, Proceedings of the Second International Conference on Soft Computing for Problem Solving (Soc Pro S 2012), December 28-30, 2012 Advances in Intelligent Systems and Computing, 236, 353-361.

Atshan, W.G. (2008) Fractional Calculus on a Subclass of Spiral-Like Functions Defined by Komatu Operator,International Mathematical Forum 3(32),1587-1594.

Bansal, D., (2011) Fekete -Szeg problem for a new class of analytic function, International Journal of Mathematics and Mathematical Science,article ID 143096,5 pages.

Sokol,J.,(2006) On sufficient condition for starlikeness of certain integral of analytic function, Journal of Mathematics and Applications, 28, 127-130.

Komatu,Y.(1990)On analytic prolongation of a family of integral operators, Mathematica(Cluj), 32(55), 141-145.

Li,J.L.,(1994)On some classes of analytic functions, Mathematica Japonica,40(3),523-529.

Libera, R. J. and Zlotkiewicz, E. J. (1983) Coefficient bounds for the inverse of a function with derivative inρ, Proceedings of the American Mathematical Society, 87(2), 251-257.

Ma, W., and Minda, D. (1994) 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. editors) Conference proceeding and lecture notes in analysis, International press, Cambridge, Massachusetts, Vol. I, 157-169.

Murugusundaramoorthy, G., Srivastava, H.M. (2004) Neighborhood of certain classes of analytic functions of complex order, Journal of Inequalities in Pure and Applied Mathematics, 5(2), article(24).

Ponnusamy, S. and Ronning, F. (2008) Integral transforms of a class of analytic functions, Complex Variables and El liptic E qu ations, 53(5), 423-434.

Ponnusamy,S.(1996)Neighborhoods and Carathodory functions, Journal of Analysis,4, 41-51.

Rusheweyh, St. (1982) Convolution in Geometric Function Theory, L e s Presses del’ Montreal.

Rusheweyh, St., Stankiewicz, J. (1985) Subordination under convex univalent function, Bul l. Pol. Aca d . Sci. Math. 33, 499-502.

Saigo,M.(1978)Aremark on integral operators involving the Gauss hypergeometric functions, Math. Rep. Col lege General Ed. Kyushu Univ. 11, 135-143.

Silverman, H. (1991) A survey with open problems on univalent functions whose coefficients are negative, Roc k y Mountain J. Math., 21, 1099-1125.

Silverman, H. (1997) Integral means for univalent functions with negative coefficients, Houston J. Math., 23, 169-174.

Srivastava, H.M., Saigo, M. and Owa, S. (1988) A class of distortion theorems involving certain operators of fractional calculus of starlike functions, J. Math. Anal. and Appl. 131, 412-420.

Swaminathan, A. (2010) Sufficient conditions for hypergeometric functions to being a certain class of analytic functions, Computers and Mathematics with Applications, 59(4), 1578-1583.

Vijaya,K. and Deepa,K.(2013) Neighborhood and partial sums results on the class of starlike functions involving Dziok-Srivastava operator, Stud. Univ. Babes-Bolyai Math., 58(2), 171180.



  • There are currently no refbacks.