Some basic properties of certain subclass of harmonic univalent functions

In this paper, a new subclass of complex-valued harmonic univalent functions f(z)=h(z)+g(z)¯¯¯¯¯¯¯¯¯ in the open disk U={z:z∈C and |z|<1} defined by using a linear operator. We investigate coefficient condition, extreme points, distortion and convex combination for this subclass.

In this paper, using Differential operator a certain subclass of harmonic univalent functions in the unit disc U = {z ∈ C : |z| < 1} is investigated. Some properties such as coefficient bounds, convex combination, extreme points and convolution conditions of this class are obtained. The newly introduced subclass of harmonic univalent functions is more general than the subclasses earlier found in the literature.

Let SH be the class of functions f = h+g that are harmonic univalent and sense-preserving in the open unit disk U = { z : |z| < 1} for which f (0) = f'(0)-1=0. In this paper, we introduce and study a subclass H( α, β) of the class SH and the subclass NH( α, β) with negative coefficients. We obtain basic results involving sufficient coefficient conditions for a function in the subclass H( α, β) and we show that these conditions are also necessary for negative coefficients, distortion bounds, extreme points, convolution and convex combinations. In this paper an attempt has also been made to discuss some results that uncover some of the connections of hypergeometric functions with a subclass of harmonic univalent functions.

We investigate some properties of a new subclass of harmonic univalent functions defined by multiplier transformation. We obtain coefficient conditions, extreme points, distortion bounds, convolution, and convex combination for the above subclass of harmonic functions.

The purpose of the present paper is to introduce a new subclass of harmonic univalent functions associated with a $q$-Ruscheweyh derivative operator. A necessary and sufficient convolution condition for the functions to be in this class is obtained. Using this necessary and sufficient coefficient condition, results based on the extreme points, convexity and compactness for this class are also obtained.

In this paper, a class of complex-valued harmonic univalent functions f (z) in the open disk U is defined by fractional calculus operator. We obtained coefficient bounds, distortion inequalities, convex combination, extreme points and convolution conditions for this class.

In the present paper, we obtain some inclusion relations and convolution properties for certain subclasses of analytic functions in the unit disk which are defined by the generalized Salagean operator. Relevant connections of the results presented here with those obtained in earlier works are pointed out.

In this paper, we introduce new subclasses of analytic and p-valent functions related to starlike, convex, close-to-convex, and quasi-convex functions by using a p-valent analog of the Tremblay fractional derivative operator. Inclusion relationships for these subclasses are established.

By making use of the operator $B_\nu^c$ defined by the generalized Bessel functions of the first kind, the authors introduce and investigate several new subclasses of starlike, convex, close-to-convex and quasi-convex functions. The authors establish inclusion relationships associated with the aforementioned operator. Some interesting corollaries and consequences of the main inclusion relationships are also considered.

Some Properties of Certain Subclasses of Meromorphic Multivalent Functions of Complex Order Defined by Certain Linear Operator

Making use of a linear operator, which is defined by the Hadamard product, we introduce and study a subclassYa,c+(A,B;p,λ,α)of the classA+(p). In this paper, we obtain the coefficient inequality, distortion theorem, radius of convexity and starlikeness, neighborhood property, modified convolution properties of this class. Furthermore, an application of fractional calculus operator is given. The results are presented here would provide extensions of some earlier works. Several new results are also obtained.

Let be a harmonic univalent and orientation-preserving function on the unit disk, where h and g are analytic. We first give an example to show that there can be no upper-bound on the valency of h. Then we show that h is Bloch if, and only if, h is BMOA if, and only if, f is BMOA and we show that log h is Bloch if, and only if, log h is B MOA. Finally, we give sharp estimates for the Bloch-norm and BMOH2-norm of f when f maps the unit disk onto the unit disk.

Quantum calculus or q-calculus plays an important role in hypergeometric series, quantum physics, operator theory, approximation theory, sobolev spaces, geometric functions theory and others. But role of q-calculus in the theory of harmonic univalent functions is quite new. In this paper, we make an attempt to connect quantum calculus and harmonic univalent starlike functions. In particular, we introduce and investigate the properties of q-harmonic functions and q-harmonic starlike functions of order ?.

Shift operators on harmonic Hilbert function spaces on real balls and von Neumann inequality

The aim of this paper is twofold. First, we investigate the properties of the composition of harmonic mappings with harmonic mappings, and the composition of biharmonic mappings with harmonic mappings. Second, we consider the Goodman-Saff conjecture for biharmonic mappings in the unit disk. In fact, we show that the answer to the Goodman-Saff conjecture is positive for a special class of univalently biharmonic mappings which contains the set of all harmonic univalent mappings.