The Radius of Convexity of Partial Sums of Convex Functions in One Direction

“…Clearly, G(1) ≡ G which was introduced by Ozaki [22] and proved that functions in G are univalent in D. Later on, Singh and Singh [32] proved that functions in G are starlike in D. By Umezawa [33], each function in G maps every D r onto a domain which is convex in one direction. For more informations about the class G in different contexts we refer [18,24,26,30].…”

Section: The Class G(c)mentioning

confidence: 99%

“…As a motivation from their work, we have studied here the growth, covering and area problems for the class of functions f in F α G . The following lemma from [18] is useful in this section (see also [20]). Lemma 4.1.…”

Section: Growth Covering and Area Theorems For F αmentioning

confidence: 99%

Planar harmonic mappings in a family of functions convex in one direction

Maharan

Kumar

2021

Filomat

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Let D := {z ? C : |z| < 1} be the open unit disk, and h and 1 be two analytic functions in D. Suppose that f = h + ?g is a harmonic mapping in D with the usual normalization h(0) = 0 = g(0) and h'(0) = 1. In this paper, we consider harmonic mappings f by restricting its analytic part to a family of functions convex in one direction and, in particular, starlike. Some sharp and optimal estimates for coefficient bounds, growth, covering and area bounds are investigated for the class of functions under consideration. Also, we obtain optimal radii of fully convexity, fully starlikeness, uniformly convexity, and uniformly starlikeness of functions belonging to those family.

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“…The class G(a) has been studied extensively by Kargar et al [11], Maharana et al [16], Obradović et al [17], and Ponnusamy and Sahoo [20]. It is well-known that the logarithmic coefficients have had great impact in the development of the theory of univalent functions.…”

Section: Introductionmentioning

confidence: 99%

On logarithmic coefficients of certain starlike functions related to the vertical strip

Kargar

2018

J Anal

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In the present paper two certain subclasses of the starlike functions associated with the vertical strip are considered. The main aim of this paper is to investigate some basic properties of these classes such as, subordination relations, sharp inequalities for sums involving logarithmic coefficients and estimate of logarithmic coefficients for functions belonging to these subclasses.2010 Mathematics Subject Classification. 30C50; 30C45.

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The Radius of Convexity of Partial Sums of Convex Functions in One Direction

Cited by 13 publications

References 10 publications

Pre-Schwarzian norm estimates for the class of janowski starlike functions

Pre-Schwarzian norm estimates for the class of janowski starlike functions

Planar harmonic mappings in a family of functions convex in one direction

On logarithmic coefficients of certain starlike functions related to the vertical strip

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