A subclass of parabolic starlike and uniformly convex functions

Let A be the class of analytic functions in the open unit disk U. A function f in A satisfying the normalization is said to be in the class SP_n if Dⁿf is a parabolic starlike function, where Dⁿ is a notation of the Salagean operator. In this paper, several basic properties and characteristics of the class SP_n are investigated. These include subordination, convolution properties, class-preserving integral operators, and Fekete-Szegö problems.     

Some properties of two subclasses of k-fold symmetric functions associated with Srivastava-Attiya operator

In the present paper, by using the Srivastava-Attiya operator, we define two new subclasses of k-fold symmetric analytic functions. Some interesting properties of these subclasses such as integral representations, extreme points, close convex hulls and subordinations are obtained, which generalize and refine some previous results.     

Sandwich-type theorems for multivalent functions associated with the Srivastava-Attiya operator

In the present paper, we investigate some subordination- and superordination-preserving properties for certain classes of analytic and multivalent functions in the open unit disk, which are associated with such multiplier transformations as the Srivastava-Attiya operator. Various sandwich-type theorems for functions belonging to these classes are also obtained.     

Double Subordination Preserving Properties for a New Generalized Srivastava-Attiya Integral Operator

The authors obtain subordination and superordination preserving properties for a new defined generalized operator involving the Srivastava-Attiya integral operator.Differential sandwich-type theorems f...     

The order of starlikeness of the class of uniformly starlike functions

We investigate classes of k‐uniformly starlike functions which generalize the class UST introduced by Goodman in 1991. Obtained results enable us to solve the problem of finding the largest such that the class of k‐uniformly starlike functions is contained in the class of starlike functions of order α.     

Some inclusion relationships associated with the Komatu integral operator

In this paper we introduce and study some new subclasses of starlike, convex, close-to-convex and quasi-convex functions defined by the Komatu integral operator. Inclusion relationships are established and integral operator of functions in these subclasses is discussed.     

On classes of analytic functions defined by convolution with incomplete beta functions

Carlson and Shaffer [SIAM J. Math. Anal. 15 (1984) 737-745] defined a convolution operator L(a,c) on the class A of analytic functions involving an incomplete beta function ?(a,c;z) as L(a,c)f=?(a,c)?f. We use this operator to introduce certain classes of analytic functions in the unit disk and study their properties including some inclusion results, coefficient and radius problems. It is shown that these classes are closed under convolution with convex functions.     

Classes of analytic functions associated with the Choi-Saigo-Srivastava operator

We investigate several properties of the linear Choi-Saigo-Srivastava operator and associated classes of analytic functions which were introduced and studied by J.H. Choi, M. Saigo and H.M. Srivastava [J.H. Choi, M. Saigo, H.M. Srivastava, Some inclusion properties of a certain family of integral operators, J. Math. Anal. Appl. 276 (2002) 432-445]. Several theorems are an extension of earlier results of the above paper.     

Absolutely convex,uniformly starlike and uniformly convex harmonic mappings

In this paper, we prove necessary and sufficient conditions for a sense-preserving harmonic function to be absolutely convex in the open unit disc. We also estimate the coefficient bound and obtain growth, covering and area theorems for absolutely convex harmonic mappings. A natural generalization of the classical Bernardi-type operator for harmonic functions is considered and its connection between certain classes of uniformly starlike harmonic functions and uniformly convex harmonic functions is also investigated. At the end, as applications, we present a number of results connected with hypergeometric and polylogarithm functions.     

Coefficient bounds for a subclass of starlike functions of complex order

In the present work, we determine coefficient bounds for functions in certain subclass of starlike functions of complex order b, which are introduced here by means of a multiplier differential operator. Several corollaries and consequences of the main results are also considered.     

Inclusion properties for certain classes of meromorphic functions associated with the Choi–Saigo–Srivastava operator

The purpose of the present paper is to introduce several new classes of meromorphic functions defined by using a meromorphic analogue of the Choi–Saigo–Srivastava operator for analytic functions and investigate various inclusion properties of these classes. Some interesting applications involving these and other classes of integral operators are also considered.     

An isoperimetric inequality for uniformly log-concave measures and uniformly convex bodies

We prove an isoperimetric inequality for the uniform measure on a uniformly convex body and for a class of uniformly log-concave measures (that we introduce). These inequalities imply (up to universal constants) the log-Sobolev inequalities proved by Bobkov, Ledoux [S.G. Bobkov, M. Ledoux, From Brunn-Minkowski to Brascamp-Lieb and to logarithmic Sobolev inequalities, Geom. Funct. Anal. 10 (5) (2000) 1028-1052] and the isoperimetric inequalities due to Bakry, Ledoux [D. Bakry, M. Ledoux, Lévy-Gromov's isoperimetric inequality for an infinite-dimensional diffusion generator, Invent. Math. 123 (2) (1996) 259-281] and Bobkov, Zegarliński [S.G. Bobkov, B. Zegarliński, Entropy bounds and isoperimetry, Mem. Amer. Math. Soc. 176 (829) (2005), x+69]. We also recover a concentration inequality for uniformly convex bodies, similar to that proved by Gromov, Milman [M. Gromov, V.D. Milman, Generalization of the spherical isoperimetric inequality to uniformly convex Banach spaces, Compos. Math. 62 (3) (1987) 263-282].     

Coefficient bounds for some families of starlike and convex functions of complex order

In the present work, the authors determine coefficient bounds for functions in certain subclasses of starlike and convex functions of complex order, which are introduced here by means of a family of nonhomogeneous Cauchy–Euler differential equations. Several corollaries and consequences of the main results are also considered.     

Closure properties of operators on the Ma-Minda type starlike and convex functions

A normalized univalent function f is called Ma-Minda starlike or convex if zf^′(z)/f(z)?φ(z) or 1+zf^″(z)/f^′(z)?φ(z) where φ is a convex univalent function with φ(0)=1. The class of Ma-Minda convex functions is shown to be closed under certain operators that are generalizations of previously studied operators. Analogous inclusion results are also obtained for subclasses of starlike and close-to-convex functions. Connections with various earlier works are made.     

Inclusion and argument properties for certain subclasses of meromorphic functions associated with a family of multiplier transformations

Making use of a multiplier transformation, which is defined here by means of the Hadamard product (or convolution), the authors introduce some new subclasses of meromorphic functions and investigate their inclusion relationships and argument properties. Some integral-preserving properties in a given sector are also considered.     

On classes of analytic functions related to conic domains

We introduce classes of analytic functions related to conic domains, using a new linear multiplier fractional differential operator (n∈N₀={0,1,…}, 0?α<1, λ?0), which is defined as

D⁰f(z)=f(z),     

Inclusion and neighborhood properties for certain classes of multivalently analytic functions of complex order associated with the convolution structure

Making use of the familiar convolution structure of analytic functions, in this paper we introduce and investigate two new subclasses of multivalently analytic functions of complex order. Among the various results obtained here for each of these function classes, we derive the coefficient inequalities and other interesting properties and characteristics for functions belonging to the class introduced here.