On a Subclass of Analytic Functions Related to a Hyperbola

The object of the present investigation is to solve Fekete-Szego problem and determine the sharp upper bound to the second Hankel determinant for a new class of analytic functions in the unit disk. We also obtain a sufficient condition for an analytic function to be in this class.

[1]  R. R. London,et al.  Fekete-Szego Inequalities for Close-to-Convex Functions , 1993 .

[2]  M. Fekete,et al.  Eine Bemerkung Über Ungerade Schlichte Funktionen , 1933 .

[3]  B. C. Carlson,et al.  Starlike and Prestarlike Hypergeometric Functions , 1984 .

[4]  Matti Vuorinen,et al.  Univalence and Convexity Properties for Gaussian Hypergeometric Functions , 2001 .

[5]  Sanford S. Miller,et al.  Univalence of Gaussian and confluent hypergeometric functions , 1990 .

[6]  I. S. Jack.  Functions Starlike and Convex of Order α , 1971 .

[7]  Estimate on the second Hankel functional for functions whose derivative has a positive real part , 2008 .

[8]  Maslina Darus,et al.  Coefficient inequality for a function whose derivative has a positive real part , 2006 .

[9]  Richard J. Libera,et al.  Coefficient bounds for the inverse of a function with derivative in . II , 1983 .

[10]  B. S. Mehrok,et al.  A coefficient inequality for certain classes of analytic functions , 1969 .

[11]  Edmund Taylor Whittaker,et al.  A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions; with an Account of the Principal Transcendental Functions , 1920, Nature.

[12]  M. Vuorinen,et al.  Starlikeness of the Gaussian hypergeometric functions , 2010 .

[13]  A. Pfluger.  The Fekete-Szegö inequality by a variational method , 1985 .

[14]  Syed Tauseef Mohyud-Din,et al.  A Coefficient Inequality for Certain Classes of Analytic Functions , 2012 .

[15]  Wolfram Koepf,et al.  On the Fekete-Szegö problem for close-to-convex functions II , 1987 .

[16]  Richard J. Libera,et al.  Early coefficients of the inverse of a regular convex function , 1982 .

[17]  A. Pfluger.  The fekete—szegö inequality for complex parameters , 1986 .

[18]  T. Macgregor.  Functions whose derivative has a positive real part , 1962 .

[19]  Hari M. Srivastava,et al.  Univalent and Starlike Generalized Hypergeometric Functions , 1987, Canadian Journal of Mathematics.

[20]  Stephan Ruscheweyh.  NEW CRITERIA FOR UNIVALENT FUNCTIONS , 1975 .

[21]  Yong Chan Kim,et al.  A general approach to the Fekete-Szegö problem , 2007 .

[22]  S. Ponnusamy,et al.  On the Fekete-Szeg\"o problem for concave univalent functions , 2010, 1011.3887.