A unified class of analytic functions involving a generalization of the Srivastava-Attiya operator

In this paper, we present a unified class of analytic functions defined by a new convolution operator J ( λ p ) , ( µ q ) , b s , a , λ introduced recently by Srivastava and Gaboury (2014) which generalizes the well-known Srivastava-Attiya operator investigated by Srivastava and Attiya (2007). We derive coefficient inequalities, growth and distortion theorems, extreme points and Fekete-Szego problem for this new function class.

[1]  A. M. Mathai,et al.  The H-Function: Theory and Applications , 2009 .

[2]  Hari M. Srivastava,et al.  Sandwich-type theorems for multivalent functions associated with the Srivastava-Attiya operator , 2010, Appl. Math. Comput..

[3]  A. K. Mishra,et al.  The fekete-szegö-problem for a subclass of close-to-convex functions , 2001 .

[4]  N. Ayırtman,et al.  Univalent Functions , 1965, Series and Products in the Development of Mathematics.

[5]  Hari M. Srivastava,et al.  A New Family of the λ -Generalized Hurwitz-Lerch Zeta Functions with Applications , 2014 .

[6]  Hari M. Srivastava,et al.  An integral operator associated with the Hurwitz–Lerch Zeta function and differential subordination , 2007 .

[7]  A. W. Kemp,et al.  A treatise on generating functions , 1984 .

[8]  Hari M. Srivastava,et al.  The Hardy Space of Analytic Functions Associated with Certain One-Parameter Families of Integral Operators , 1993 .

[9]  Hari M. Srivastava,et al.  The H-functions of one and two variables, with applications , 1982 .

[10]  Hari M. Srivastava,et al.  Argument estimates of certain analytic functions defined by a class of multiplier transformations , 2003 .

[11]  Hari M. Srivastava,et al.  Series Associated with the Zeta and Related Functions , 2001 .

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

[13]  H. Srivastava,et al.  A new class of analytic functions defined by means of a generalization of the Srivastava-Attiya operator , 2015 .

[14]  Hari M. Srivastava,et al.  Some inclusion properties of a certain family of integral operators , 2002 .

[15]  Hari M. Srivastava,et al.  Integral and computational representations of the extended Hurwitz–Lerch zeta function , 2011 .

[16]  Hari M. Srivastava,et al.  Classes of analytic functions associated with the generalized hypergeometric function , 1999, Appl. Math. Comput..

[17]  H. Srivastava,et al.  Zeta and q-Zeta Functions and Associated Series and Integrals , 2011 .

[18]  H. M. Srivastava,et al.  A new class of analytic functions defined by means of a convolution operator involving the Hurwitz–Lerch Zeta function , 2007 .

[20]  Hari M. Srivastava,et al.  Certain Subclasses of Analytic Functions Associated with the Generalized Hypergeometric Function , 2003 .

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

[22]  J. K. Prajapat,et al.  Double subordination preserving properties for a new generalized Srivastava-Attiya integral operator , 2012 .

[23]  Hari M. Srivastava,et al.  Some formulas for the Bernoulli and Euler polynomials at rational arguments , 2000, Mathematical Proceedings of the Cambridge Philosophical Society.

[24]  S. D. Bernardi,et al.  Convex and starlike univalent functions , 1969 .

[25]  Hari M. Srivastava Generating relations and other results associated with some families of the extended Hurwitz-Lerch Zeta functions , 2013 .

[26]  H. Srivastava,et al.  A new class of generalized close-to-starlike functions defined by the Srivastava-Attiya operator , 2013 .

[27]  Hari M. Srivastava,et al.  Two-sided inequalities for the extended Hurwitz-Lerch Zeta function , 2011, Comput. Math. Appl..

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

[29]  Hari M. Srivastava,et al.  New Expansion Formulas for a Family of the iλ-Generalized Hurwitz-Lerch Zeta Functions , 2014, Int. J. Math. Math. Sci..

[30]  Hari M. Srivastava,et al.  Some Generalizations and Basic (or q-) Extensions of the Bernoulli, Euler , 2011 .

[31]  M. Inoue,et al.  Soil degradation and prevention in greenhouse production , 2013, SpringerPlus.