Coefficients bounds in some subclass of analytic functions


  • Janusz Sokol Rzeszow University of Technology
  • Deepak Bansal



Analytic function, Subordination, Starlike function,


In this paper we consider a class of analytic functions introduced by Mishra and Gochhayat, {\it Fekete-Szeg\"o problem for a class defined by an integral operator}, Kodai Math. J., 33(2010) 310--328, which is connected with $k$-starlike functions through Noor operator. We find inclusion relations and coefficients bounds in this class.

Author Biographies

Janusz Sokol, Rzeszow University of Technology

Department of Mathematics, Rzeszów University of Technology, al. Powsta´nców Warszawy 12, 35-959 Rzeszów,Poland.

Deepak Bansal

Department ofMathematics, College of Engg. and Technology, Bikaner 334004, Rajasthan, India.


G. D. Anderson, M. K. Vamanamurth and M. K. Vuorinen, Conformal Invariants, Inequalities and Quasiconformal Maps, Wiley-Interscience, 1997.

R. Bharati, R. Parvatham and A. Swaminathan, On subclasses of uniformly convex functions and corresponding class of starlike functions, Tamkang J. Math., 28 (1) (1997), 17--32.

P. L. Duren, Univalent Functions, Springer-Verlag, Berlin, 1983.

A. W. Goodman, On uniformly convex functions, Ann. Polon. Math., 56(1991) 87--92.

S. Kanas, Stability of convolution and dual sets for the class of $k$-uniformly convex and $k$-starlike functions, Folia Sci. Univ. Tech. Resov., 170(1998), 51--64.

S. Kanas, Techniques of the differential subordination for domains bounded by conic sections, IJMMS, 38(2003), 2389--2400.

S. Kanas, Coefficient estimates in subclasses of the Caratheodory class related to conical domains, Acta Math. Univ. Comenian, 74(2005), 149--161.

S. Kanas and H. M. Srivastava, Linear operators associated with $k$-uniformly convex functions, Integral Transform. Spec. Funct., 9(2) (2000), 121--132.

S. Kanas and T. Sugawa, On conformal representations of the interior of an ellipse, Ann. Acad. Sci. Fenn. Math., 31(2006), 329--348.

S. Kanas and A. Wisniowska, Conic regions and $k$-uniform convexity II, Folia Sci. Univ. Tech. Resov., 170(1998), 65--78.

S. Kanas, A. Wisniowska, Conic regions and $k$-uniform convexity, J. Comput. Appl. Math., 105(1999),327--336.

S. Kanas and A. Wisniowska, Conic regions and $k$-starlike functions, Rev. Roumaine Math. Pures Appl., 45(2000), 647--657.

A. Lecko and A. Wisniowska, Geometric properties of subclasse of starlike functions, J. Comp. Appl. Math.,155(2003), 383--387.

W. Ma and D. Minda, Uniformly convex functions, Ann. Polon. Math., 57(2) (1992), 165--175.

A. K. Mishra and P. Gochhayat, Fekete-Szego problem for a class defined by an integral operator, Kodai Math. J.,33(2010) 310--328.

K. I. Noor, On new class of integral operator, J. Natur. Geom., 16(1999), 71--80.

W. Rogosinski, On the coefficients of subordinate functions, Proc. London Math. Soc., 48(1943), 48--82.

F. Ronning, Uniformly convex functions and a corresponding class of starlike functions, Proc. Amer. Math. Soc.118(1993), 189--196.

St. Ruscheweyh, Convolutions in Geometric Function Theory, Sem. Math. Sup. 83, Presses Univ. Montreal, 1982.

St. Ruscheweyh, New criteria for univalent function, Proc. Amer. Math. Soc., 49(1975), 109--115.

St. Ruscheweyh and T. Sheil-Small, Hadamard product of schlicht functions and the Poyla-Schoenberg conjecture, Comm. Math. Helv., 48(1973), 119--135.

H. M. Srivastava, Generalized hypergeometric functions and associated families of $k$-starlike functions, Gen.Math., 15 (2-3) (2007), 201--226.

K. G. Subramanian, G. Murugusundaramoorthy, P. Balasubrahmanyam and H. Silverman, Subclasses of uniformly convex and uniformly starlike functions, Math. Japon., 42 (3)(1995), 517--522.




How to Cite

Sokol, J., & Bansal, D. (2012). Coefficients bounds in some subclass of analytic functions. Tamkang Journal of Mathematics, 43(4), 621-630.