Page 361 some new properties of support points for compact families of univalent functions in the unit disc. Order of starlikeness for multipliers of univalent functions. For k0, p 1,q 0, this class reduces to sh d the class of univalent harmonic starlike functions of order d which was studied by jahangiri 2 and for k 0 p 2, x 1, it reduces to the class kh d, the class of univalent harmonic convex function of order d. Univalent function, starlike function, convex function, sections, partial. Sis starlikeinthedisk z starlikeness of f see hayman 4 for definitions. Pdf geometric properties of partial sums of univalent functions. As a consequence, conditions for starlikeness of functions defined by integral operators are obtained. Important geometric subclasses of s h and s h 0, such as convex, closetoconvex, starlikeness and typically real harmonic functions, are discussed by clunie and sheilsmall. On harmonic combination of univalent functions obradovic, m. Ponnusamy, title injectivity and starlikeness of sections of a class of univalent functions, year 20. S is called starlike if fd is starlike with respect to the origin, i. Let denote the class of biunivalent functions in, given by equation 1. Abstract let be the class of functions analytic and univalent in the unit disk function in that are starlike and convex. Introduction let adenote the class of normalized analytic functions of the form f.
Coefficient characterizations and sections for some univalent functions. Univalent, starlike, convex and closetoconvex functions, subordina. For many interesting results and expositions on planar harmonic univalent mappings, we refer the book of duren. Certain conditions for starlikeness of analytic functions.
Coefficient characterizations and sections for some. Let s be the class of all normalized analytic andunivalentfunctions intheunitdisk d. A function is said to be biunivalent in if both and are univalent in. We close this section with several observations concerning the function fpz of 4. At the end of section 2, we also consider estimates of the type 2. Pdf starlikeness of sections of univalent functions. Injectivity and starlikeness of sections of a class of. We observe that in contrast to the class s, the extremal functions for the bound of higher order schwarzian derivatives for the class sc of convex univalent functions are dierent. Coefficient estimates for starlike and convex classes of. Pdf coefficient characterizations and sections for some. Pdf is not rendering correctly, you can download the pdf file here. The class of univalent functions in a is traditionally denoted by s. Logarithmic coefficients and a coefficient conjecture for univalent.
An analytic function is subordinate to an analytic function, written, provided there is an analytic function defined on with and satisfying lewin investigated the class of biunivalent functions and obtained a bound. Sufficient conditions are obtained to ensure starlikeness of positive order for analytic functions defined in the open unit disk satisfying certain thirdorder differential inequalities. Analytic, univalent, starlike, closetoconvex and convex functions, co efficient inequality, area theorem, radius of univalency, subordination, convolution and the. Let s be the standard subclass of s of starlike functions. Ronning, uniformly starlike and convex functions and other related classes of univalent functions. Inthispaper,we determine condition so that each section snf,zoff. This power series for the largest univalent function suggests immediately. In this section, we first prove the following result theorem 4 below, which involves the already. Injectivity of sections of univalent harmonic mappings. Closetoconvexity, starlikeness, and convexity of certain. A thirdorder differential equation and starlikeness of a double integral operator ali, rosihan m. We prove some new sufficient conditions for functions to be pvalently starlike in the unit disc.
The purpose of this paper is to introduce a class of functions. Study of some subclasses of univalent functions and. Request pdf injectivity and starlikeness of sections of a class of univalent functions let g denote the class of locally univalent normalized analytic functions f in the unit disk vertical bar. W goodman, univalent functions, mariner publishing company, inc, u. Harmonic univalent, starlike, closetoconvex and convex mappings. All functions in f b are univalent and starlike if and only if e n for every n. Symmetric conformable fractional derivative of complex. Geometric conditions forstarlikenessand convexity of. Journal of inequalities and applications on uniformly univalent functions with respect to symmetrical points khalida inayat noor 0 0 department of mathematics, comsats institute of information technology, park road, islamabad, pakistan in this paper, we define and study some new subclasses of starlike and closetoconvex functions with respect to symmetrical points. Radii of starlikeness and convexity of some special functions.
In particular, if the function g is univalent in u, the subordination. By specializing b, the results reduce to those of some wellknown families. Some starlikeness conditions for the analytic functions. Conditions for starlikeness of multivalent functions. Some consequences of the obtained result are also considered. Disk of convexity of sections of univalent harmonic functions.
Geometric conditions for starlikeness and convexity of univalent functions. On a class of analytic functions governed by subordination. We generate various starlike and convex univalent functions and polynomials through the location of their zeros andor poles. A function fz meromorphic in a domain \d\subset \mathbb c\ is said to be pvalent in d if for each w the equation \fzw\ has at most p roots in d, where roots are counted in accordance with their multiplicity, and there is some v such that the equation \fzv\ has exactly p roots in d. It turns out that these starlike functions are extremal, in the whole class of univalent functions, for a functional which involves the schwarzian derivative. Ann university, marie curiesklodowska section a, 531999 95105. The extreme points, distortion properties, order of starlikeness, and radius of convexity for such families are determined. Pdf sections of univalent harmonic mappings researchgate. Starlikeness of sections of univalent functions, rocky mountain j.
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