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Title of Thesis

Some Classes of Generalized Convex and Related Functions

Author(s)

Wasim Ul Haq

Institute/University/Department Details
Department of Mathematics / Comsats Institute of Information Technology, Islamabad
Session
2011
Subject
Mathematics
Number of Pages
136
Keywords (Extracted from title, table of contents and abstract of thesis)
Classes, Special, Functions, Rotations, Convex, Analytic, Generalized, Techniques, Related, Boundary, Univalent

Abstract
In this thesis, certain classes of analytic functions, such as , ,UK ( , ) η κ − λ α − 􀁩 1 2 UQC ( , ) Rk ( , , ) η κ λ α , N􀁩k (η,ρ ,β ) , ( , ) k R m ρ and , p ( , , , , ) k Rλ a b c A B are introduced.These classes generalize the concepts of uniformly close-to-convex and quasi-convex, bounded turning, strongly close-to-convex, bounded boundary rotations and bounded radius rotations.These classes are special generalizations of convex and related functions.The techniques of convolution and differential subordination are employed to investigate certain problems such as inclusion results, radius problems, arc lengths, growth rate of coefficients and Hankel determinant problems and other several interesting properties of the above mentioned classes.Some well-known results appear as special cases from our main results.

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S. No. Chapter Title of the Chapters Page Size (KB)
1 0 CONTENTS

 

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1

ELEMENTARY CONCEPTS FROM GEOMETRIC FUNCTION THEORY

1.1 Introduction
1.2 Analytic and univalent functions
1.3 Functions with positive real part and related classes
1.4 Some basic subclasses of univalent functions
1.5 The class of bounded boundary rotation and related topics
1.6 Differential subordination
1.7 Convolution (Hadamard product) and certain linear operators

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3 2 ONCLASSESOF -UNIFORMLY CLOSE-TO-CONVEX AND RELATED FUNCTIONS

2.1 The class of -uniformly close-to-convex functions of complex order
2.2 The class . UQC(, )
2.3 Some applications of convolution invariance

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4 3 SOME PROPERTIES OF A SUBCLASS OF ANALYTIC FUNCTIONS

3.1 Certain properties of the class]Rk(1, 2, )

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5 4 ON A CERTAIN CLASS OF ANALYTIC FUNCTIONS AND HANKEL DETERMINANT PROBLEM

4.1 Some properties of the class]Nk(, , )
4.2 Hankel determinant problem

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6 5 SOME APPLICATIONS OF RUSCHEWEYH DERIVATRIVES

5.1 Certain analytic functions defined by Rusheweyh derivatives

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7 6 ONCERTAINCLASSOFP-VALENT FUNCTIONS DEFINED BY SOME INTEGRAL OPERATOR

6.1 An integral operator
6.2 A class of analytic p-valent functions
6.3 Some inclusion results

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REFERENCES

 

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