The rational cubic function with three parameters has been extended to rational bi-cubic function to visualize the shape of regular convex surface data. The rational bi-cubic function involves six parameters in each rectangular patch. Data dependent constraints are derived on four of these parameters to visualize the shape of convex surface data while other two are free to refine the shape of s...

We deal with kernel convergence of domains in Cn which are biholomorphically equivalent to the unit ball B. We also prove that there is an equivalence between the convergence on compact sets of biholomorphic mappings on B, which satisfy a growth theorem, and the kernel convergence. Moreover, we obtain certain consequences of this equivalence in the study of Loewner chains and of starlike and co...

The main aim of this paper is to use the method of differential subordination to obtain a number of sufficient conditions for a normalized analytic function to be univalent or starlike in the unit disc. In particular, we find a condition on β so that each normalized analytic function f satisfying the condition ∣∣∣1 + zf ′′(z) 2f ′(z) − zf ′(z) f(z) ∣∣∣ < β, z ∈ Δ implies that f is univalent or ...

In this paper, we introduce a family of harmonic parabolic starlike functions of complex order in the unit disc and coefficient bounds, distortion bounds, extreme points, convolution conditions and convex combination are determined for functions in this family. Further results on integral transforms are discussed. Consequently, many of our results are either extensions or new approaches to thos...

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 (...

The pre-Schwarzianand Schwarzian derivatives of analytic functions f are defined in U, where U is the open unit disk. pre-Schwarzian as well popular tools for studying geometric properties mappings. These can also be used to obtain either necessary or sufficient conditions univalence a function f. Because computational difficulty, norm has received more attention than norm. It applications theo...

We are interested in finding the sufficient conditions on A , B , λ , b and c which ensure that the generalized Bessel functions uλ := uλ ,b,c satisfies the subordination uλ (z) ≺ (1+Az)/(1+Bz) . Also, conditions for which uλ (z) to be Janowski convex, and zuλ (z) to be Janowski starlike in the unit disk D = {z ∈ C : |z| < 1} are obtained. Mathematics subject classification (2010): 34B30, 33C10...

Two classes of univalent harmonic functions on unit disc satisfying the conditions ∑∞ n=2(n−α)(|an|+|bn|) ≤ (1−α)(1−|b1|) and ∑∞ n=2 n(n−α)(|an|+|bn|) ≤ (1−α)(1−|b1|) are given. That the ranges of the functions belonging to these two classes are starlike and convex, respectively. Sharp coefficient relations and distortion theorems are given for these functions. Furthermore results concerning th...

To obtain the main result of present paper we use technique differential subordination. As special cases our result, sufficient conditions for $f\in\mathcal A$ to be $\phi-$like, starlike and close-to-convex in a parabolic region.

In the present paper, we have established sufficient conditions for Gaus-sian hypergeometric functions to be in certain subclass of analytic univalent functions in the unit disc $mathcal{U}$. Furthermore, we investigate several mapping properties of Hohlov linear operator for this subclass and also examined an integral operator acting on hypergeometric functions.