Current Topics in Analytic Function Theory

The following sections are included:

• PREFACE

• CONTENTS

The following sections are included:

• Introduction

• Auxillary Results

• Logharmonic Disk Mappings

• Logharmonic Ring Mappings

• References

The following sections are included:

• Introduction and Definitions

• Hadamard Products of Univalent Functions

• Order of Starlikeness

• Extreme Points and Its Applications

• References

The following sections are included:

• Introduction

• A Constraint Problem in 𝒫_R

• The Constraint Coefficient Problem in S^*_R and C_R

• References

The following sections are included:

• Introduction

• Basic Properties of the Class T(α, b)

• An Application of Fractional Calculus

• Close-To-Convexity, Starlikeness and Convexity

• Acknowledgements

• References

The following sections are included:

• Introduction

• Complete Elliptic Integrals

• The Hypergeometric Function

• Quotient of Elliptic Integrals

• Perturbed Identities

• Conjectures and Open Problems

• Acknowledgements

• References

The following sections are included:

• Introduction

• Properties of the Class M_n+p−1

• Acknowledgements

• References

The following sections are included:

• Introduction and General Remarks

• The Definition of the Class 𝒫(B,b;α)

• Conditions Upon the Parameters B, b, and α

• Examples of Functions

• The Compactness of 𝒫(B, b; α)

• Convexity of the Class 𝒫(B, b; α)

• References

The following sections are included:

• Introduction and Definitions

• Preliminaries

• Univalency, Starlikeness and Convexity

• Radii of Univalence, Starlikeness and Convexity

• Relations Between the Function f_b(z) and the Classes M(α, β) and N(α, β)

• Acknowledgements

• References

The following sections are included:

• Introduction and Definitions

• A Set of Lemmas

• Main Results

• Acknowledgements

• References

The following sections are included:

• Introduction

• The Union of Two Sets

• Convex Hulls

• Three Points

• The General Case

• Conclusion

• References

The following sections are included:

• Introduction

• Probabilistic Results
  • Results in
  • Results in for 1 ≤ p < ∞

• Contractive Zero Divisors
  • Results in
  • Results in for 1 ≤ p < ∞

• Conclusions

• References

The following sections are included:

• Introduction

• Preliminaries

• Spherically Invariant Differential Operators

• Spherical Convexity

• Uniform Local Spherical Convexity

• Connection with Normal Functions

• Another Instance of Spherical Linear Invariance

• Concluding Remarks

• Acknowledgements

• References

The following sections are included:

• Introduction

• Preliminaries

• A Special Differential Subordination

• Applications to Univalent Functions

• Acknowledgements

• References

The following sections are included:

• Introduction

• A Characterization of Nonlinear Functions

• Valiron's Theorem

• A Unifying Principle

• Further Results Involving the Property ȡ_M

• Acknowledgements

• References

The following sections are included:

• Introduction

• The Main Result

• Remarks and Observations

• Acknowledgements

• References

The following sections are included:

• Introduction

• Preliminaries

• Criterion for Starlikeness

• Acknowledgements

• References

The following sections are included:

• Introduction

• Main Results

• References

The following sections are included:

• Introduction

• Further Classes Related to the Classes K_n

• Some Criteria for Univalence

• Analytic Functions with Negative Coefficients

• Acknowledgements

• References

The following sections are included:

• Introduction

• The Class

• The Class C_n(p, α)

• Generalization of Theorem D and Theorem L

• The Class R_n(p, j, α)

• References

The following sections are included:

• Introduction

• Preliminary Lemmas

• Main Results

• References

The following sections are included:

• Introduction

• An Inclusion Relationship

• A Closure Property

• Acknowledgements

• References

The following sections are included:

• Definitions and Preliminaries

• General Inequalities for the Class P_n(α)

• Some Classes Related to the Class P_n(α)

• Acknowledgements

• References

The following sections are included:

• Introduction

• Generalization of the Jack-Miller-Mocanu Lemma

• Subordination Conditions for Functions with Positive Real Part

• Acknowledgements

• References

The following sections are included:

• Introduction

• The Laplace and Mellin Transforms

• Fractional Integrals and Fractional Derivatives

• Mellin Transforms of the Fractional Calculus Operators

• Representations of Fractional Calculus Operators by Laplace Transform Operators

• Acknowledgements

• References

The following sections are included:

• Introduction and Definitions

• Properties of the Class A_p(n, α)

• Some Properties of the Operator J_c

• Acknowledgements

• References

The following sections are included:

• Introduction and Preliminaries

• Some Properties of the Class M_p,n

• Acknowledgements

• References

The following sections are included:

• Introduction

• Interplay of P and W

• References

The following sections are included:

• Introduction

• Some Subclasses of S_p(α)

• Relationships Among the Classes

• References

The following sections are included:

• Introduction and Definitions

• The Main Inclusion Theorem

• Applications

• Acknowledgements

• References

The following sections are included:

• Introduction

• The Class of Functions Convex in the Direction of the Real Axis

• The Class of Convex Functions in a Half-plane

• The Class of Starlike Functions in a Half-plane

• Some Integral Formulas for the Class of Starlike Functions in a Half-plane

• Some Estimations for the Class of Starlike Functions

• References

Please refer to the full text

The following sections are included:

• Introduction and Definitions

• The Classes S_n(α)

• Acknowledgements

• References

The following sections are included:

• Introduction and Definitions

• Preliminaries

• The Radius of Starlikeness

• The Radius of Convexity

• Acknowledgements

• References

The following sections are included:

• Introduction and Preliminaries

• Main Result

• Acknowledgements

• References

The following sections are included:

• Introduction and Definitions

• The Classes A(p, n, α) and B(p, n, α)

• Distortion Theorems

• Quasi-Hadamard Products

• Acknowledgements

• References

The following sections are included:

• Introduction

• The Distortion Function Φ_K

• An Introduction to Quasihomographies

• A New Model of the Universal Teichmüller Space

• Acknowledgements

• References

The following sections are included:

• Introduction

• Growth and Distortion

• Coefficient Problem

• Residue and Area

• Convex and Starlike Subclass

• Extreme Points and Support Points

• Acknowledgements

• References

The following sections are included:

• Introduction

• Definitions and Some Classical Results

• Main Results

• Acknowledgements

• References

The following sections are included:

• Introduction and Definitions

• An Invariant Probability Measure on J(ℛ)

• Acknowledgements

• References