A starlike function f is characterized by the quantity $$zf'(z)/f(z)$$ lying in right half-plane. This paper deals with sharp bounds for certain Toeplitz determinants whose entries are coefficients of functions which takes values specific subset The results obtained include several new special cases and some known results.

We consider two parametric families of special functions: One is defined by a power series generalizing the classical Mathieu series, and other one generalized type involving factorials in its coefficients. Using criteria due to Fejér Ozaki, we provide sufficient conditions for these functions be close-to-convex or starlike inside unit disk, thus univalent. our proofs assisted symbolic computat...

By making use of the familiar Salagean derivatives, a systematic investigation of a certain subclass of uniformly convex and starlike functions with negative coefficients is presented. In addition to finding various coefficient bounds and a number of characterization and distortion theorems, a number of other potentially interesting properties of this class of functions are investigated. Finall...

In the field of Geometric Function Theory, one can not deny the importance of analytic and univalent functions. The characteristics of these functions including their taylor series expansion, their coefficients in these representations as well as their associated functional inequalities have always attracted the researchers. In particular, Fekete-Szegö inequality is one of such vastly studied a...

In recent years, the study of Hankel determinants for various subclasses normalised univalent functions f∈S given by f(z)=z+∑n=2∞anzn D={z∈C:|z|<1} has produced many interesting results. The main focus interest been estimating second determinant form H2,2(f)=a2a4−a32. A non-sharp bound H2,2(f) when f∈K(α), α∈[0,1) consisting convex order α was found Krishna and Ramreddy (Hankel starlike alpha. ...

Let denote the functions' class that is normalized, analytic, as well univalent in unit disc given by src=image/13426735_01.gif>. Convex, starlike, close-to-convex functions resemble main subclasses of src=image/13426735_02.gif>, expressed src=image/13426735_03.gif>, src=image/13426735_04.gif>, accordingly. Many mathematicians have recently studied radius problem...

The partial sums f3(z) of some extermal functions for various classes S∗, K and R of starlike functions, convex functions and functions with positive real part in the open unit disk U, respectively, are discussed. In general, the partial sums can not preserve the same character as the initial functions. The object of the present paper is to discuss the radius problems for partial sums of some e...

In the present paper, we consider a subclass of starlike functions G3/2 defined by ratio analytic representations convex and functions. The main aim is to determine bounds Fekete–Szegö-type inequalities Hankel determinants for in this class. It proved that maxH3,1(f):f∈G3/2 equal 181. f∈G3/2 are sharp.