In this paper, we introduce some classes of univalent harmonic functions with respect to the symmetric conjugate points by means subordination, analytic parts which are reciprocal starlike (or convex) functions. Further, discuss geometric properties classes, such as integral expression, coefficient estimation, distortion theorem, Jacobian growth estimates, and covering theorem.

where (a) m is nonnegative integer, (b) β= a(0)(1+a(0))/(1−|a(0)|2) and therefore, β >−1/2, (c) h and g are analytic in U , g(0)= 1, and h(0)≠ 0. Univalent logharmonic mappings on the unit disc have been studied extensively. For details see [1, 2, 3, 4, 5, 6, 7, 8]. Suppose that f is a univalent logharmonic mapping defined on the unit disc U . Then, if f(0) = 0, the function F(ζ) = log(f (eζ)) ...

Abstract: The aim of this paper is to introduce and study a new class [ ] * C A,B, δ α of Janowski QuasiConvex univalent functions of order alpha associated with Ruscheweyh derivative. Sharp coefficient bound, distortion result and some inclusion results are discussed. Invariance of [ ] * C A,B, δ α under convolution with convex functions has also been examined and some of its applications are ...

Let be the class of functions which are analytic in open unit disk and having form . Denote to for all that univalent Then, let denote bi-univalent In this paper, we obtain second Hankel determinant certain classes function defined by subordinations particular, determine initial coefficients obtained upper bound functional

Let f be a sense-preserving harmonic mapping in the unit disk. We give a sufficient condition in terms of the pre-Schwarzian derivative of f to ensure that it can be extended to a quasiconformal map in the complex plane. Introduction A well-known criterion due to Becker [5] states that if a locally univalent analytic function φ in the unit disk D satisfies (1) sup z∈D ∣∣∣∣φ′′(z) φ′(z) ∣∣∣∣ (1− ...

We define a new subclass of univalent function based on Salagean differential operator and obtained the initial Taylor coefficients using the techniques of Briot-Bouquet differential subordination in association with the modified sigmoid function. Further we obtain the classical Fekete-Szego inequality results.

In the present paper, we are defining a subclass of harmonic univalent functions with positive coefficients in unit disc U by using fractional calculus operator. Further we obtain distortion bounds, extreme points and radii of convexity for functions belonging to this class and discuss a class preserving integral operator. Here we also determine that the class studied in this paper is closed un...

In this paper we find a characterization type result for (η1,η2)-convex functions. The Fejér integral inequality related to (η1,η2)-convex functions is obtained as a generalization of Fejér inequality related to the preinvex and η-convex functions. Also some Fejér trapezoid and midpoint type inequalities are given in the case that the absolute value of the derivative of considered function is (...

Inequalities involving multipliers using the sequences {cn} and {dn} of positive real numbers are introduced for complex-valued harmonic univalent functions. By specializing {cn} and {dn}, we determine representation theorems, distortion bounds, convolutions, convex combinations, and neighbourhoods for such functions. The theorems presented, in many cases, confirm or generalize various well-kno...