کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
840033 1470505 2014 10 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Radius of convexity of partial sums of functions in the close-to-convex family
ترجمه فارسی عنوان
محدوده ای از محدب توزیع مقادیر جزئی توابع در خانواده نزدیک به محدب
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی (عمومی)
چکیده انگلیسی

Let FF denote the class of all normalized analytic functions ff that are locally univalent in the unit disk |z|<1|z|<1 satisfying the condition Re(1+zf″(z)f′(z))>−12 for |z|<1|z|<1. Functions in FF are known to be close-to-convex (univalent) in the unit disk. This class plays a crucial role in the discussion on certain extremal problems for the class of complex-valued and sense-preserving harmonic convex functions and some other related problems in determining univalence criteria for sense-preserving harmonic mappings. In this article, we show that every section of a function in the class FF is convex in the disk |z|<1/6|z|<1/6. The radius 1/61/6 is best possible. We conjecture that every section of functions in the family FF is univalent and close-to-convex in the disk |z|<1/3|z|<1/3.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 95, January 2014, Pages 219–228
نویسندگان
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