Statistical data processing of mobility curves of univalent weak bases

This paper brings a new rigorous and complete statistical approach to the data processing of the mobility curves of univalent weak bases. This approach is based on application of the least square method to the equation of the related mobility curve. Thus, an equation for the best fit is derived and its mathematical solution is found. The solution brings best estimates of the mobility curve parameters, i.e., dissociation constant K and ionic mobility of the protonated base U. Further, explicit formulas have been derived for the calculation of related statistical parameters, i.e., SDs of effective mobility s(u), of the dissociation constant s(K), and of ionic mobility of protonated base s(U). The mathematical functions used in the above approach do not impose any limitations on the data used, i.e., the mobility and pH values used may be real numbers (positive, negative, zero).     

Region of variability of two subclasses of univalent functions

Let F₁ (F₂ respectively) denote the class of analytic functions f in the unit disk |z|<1 with f(0)=0=f^′(0)−1 satisfying the condition RePf(z)<3/2 (RePf(z)>−1/2 respectively) in |z|<1, where Pf(z)=1+zf^″(z)/f^′(z). For any fixed z₀ in the unit disk and λ∈[0,1), we shall determine the region of variability for logf^′(z₀) when f ranges over the class and , respectively.     

Univalence and starlikeness of certain transforms defined by convolution of analytic functions

Let U(λ) denote the class of all analytic functions f in the unit disk Δ of the form f(z)=z+a₂z²+? satisfying the condition

     

A sharp inequality for the logarithmic coefficients of univalent functions

We prove the sharp inequality

for the logarithmic coefficients of a normalized univalent function in the unit disk.

     

On analytic functions related with generalized Robertson functions

Analytic functions f are called Robertson functions for which zf^′ is α-spiral-like. This concept is generalized by several authors and a class real, of analytic functions is introduced and studied. It is noted that the functions in are of bounded boundary rotation and consists of Robertson functions.In this paper, we use the class to define a new class of analytic functions which unifies a number of classes previously studied such as the class of close-to-convex functions of higher order. Some interesting properties of this class, including coefficient problems, inclusion results and a sufficient condition for univalency are studied.     

On the univalence of functions with logharmonic laplacian

In this paper, we prove Radó’s theorem holds for functions of the form is logharmonic. We show that if F is of the form , where is logharmonic, then F is starlike iff ψ(z)=h(z)/g(z) is starlike. In addition, when , where L is logharmonic and H is harmonic, we give the sufficient conditions for F to be locally univalent.     

Integral means and arclength inequalities for typically real logharmonic mappings

In this paper, we use star functions to conclude the integral means inequalities for typically real logharmonic mappings. Moreover, we determine the upper bound for the arclength of typically real logharmonic mappings.     

Landau’s theorem for functions with logharmonic Laplacian

In this paper, we show the existence of Landau constant for functions with logharmonic Laplacian of the form F(z) = ∣z∣²L(z) + K(z), ∣z∣ < 1, where L is logharmonic and K is harmonic. Moreover, the problem of minimizing the area is solved     

A Note on Cyclic Vectors for the Shift

We strengthen a result in the literature that gives a necessary condition for the shift on the Hardy space H 2 ( G ) of some bounded, simply connected region G to be cyclic. Part of this involves a characterization, in terms of ‘ G , of what it means for G to be the image of under a conformal map whose boundary values are univalent a.e. m (normalized Lebesgue measure on ).     

Convex and alpha-prestarlike subordination chains

In this paper we consider convex subordination chains (c.s.c.) and alpha-prestarlike subordination chains (α-p.s.c.) over (0,1] on the unit disc in the complex plane. We obtain sufficient conditions for a mapping f(z,t) to be an α-p.s.c. over (0,1], which generalize a well-known result of Ruscheweyh [St. Ruscheweyh, Convolutions in Geometric Function Theory, Les Presses de l'Université de Montreal, 1982]. We also obtain sufficient conditions for injectivity for nonanalytic mappings on the unit disc, and give certain examples of α-c.s.c. over (0,1] on the unit disc.