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العنوان
A study on subclasses of univalent and multivalent functions defined in the unit disk /
المؤلف
El-Deeb, Sheza Mohamed Abdo El-Hady.
هيئة الاعداد
باحث / شيزه محمد عبد الهادى الديب
مشرف / محمد كمال عبد السلام عوف
مشرف / رابحة محمد الأشوح
مناقش / محمد كامل جبر
مناقش / رشوان أحمد رشوان عزوز
الموضوع
Uniformly convex functions.
تاريخ النشر
2010.
عدد الصفحات
78 p. :
اللغة
الإنجليزية
الدرجة
ماجستير
التخصص
الرياضيات
تاريخ الإجازة
1/1/2010
مكان الإجازة
جامعة دمياط - كلية العلوم - الرياضيات
الفهرس
Only 14 pages are availabe for public view

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Abstract

This thesis consists of four chapters. Chapter one (Introduction), this chapter is considered as an introductory chapter for some notations and standard definitions of complex analysis which are used through out the thesis and it consists of five sections: In section 1.1, notations and standard definition of univalent functions are introduced. In section 1.2, uniformly convex and uniformly starlike functions are introduced. In section 1.3, notations and standard definition of p-valent functions are introduced. In section 1.4, linear operators associated with p-valent functions are introduced. In section 1.5, starlike functions with respect to certain points are introduced. In Chapter two, (Certain Subclasses of Uniformly Starlike and Uniformly Convex Functions Defined by Convolution), this chapter consists of nine sections. The first section is an introductory section and contains the definition of two classes , . In section 2.2, coefficient estimates for functions in the class are obtained. In section 2.3, distortion theorems for functions in the class are obtained. In section 2.4, convex linear combinations for functions in the class are discussed. In section 2.5, radii of close-to-convexity, starlikeness and convexity for functions in the class are obtained. In section 2.6, a family of integral operators for functions in the class are discussed. In section 2.7, partial sums for functions in the class are obtained. In section 2.8, integral means for functions in the class are obtained. In section 2.9, subordination results for functions in the class are obtained. In Chapter three, (Certain Classes of Univalent Functions with Negative Coefficients and n-Starlike with Respect to Certain Points), this chapter consists of six sections. The first section is an introductory section and contains the definition of the classes and defined by using Salagean operator. In section 3.2, coefficient estimates for functions in the classes and are obtained. In section 3.3, distortion theorems for functions in the classes and are obtained. In section 3.4, extreme points for functions in the classes and are obtained. In section 3.5, radii of close-to-convexity, starlikeness and convexity for functions in the class are obtained. In section 3.6, integral operators for functions in the class are discussed.