New Trends in Geometric Function Theory and Applications - Proceedings of the International Conference

After the positive settlement of Bieberbach's conjecture by Prof. Louis dé Branges, there are new avenues open for researchers in the field of Geometric Function Theory. New directions of research and new problems arising in this field are mainly considered in this proceedings. Cover Title: New Trends in Geometric Function Theory and Applications Copyright Editorial Note Professor K.S. PADMANABHAN, M.A., M.Sc., Ph.D. Photo of Prof. K.S. Padmanabhan Publications List of Padmanabhan International Conferenceon New Trends in Geometric Function Theory and Applications Photo of The Chairman and the Convenor Sponsors Photo of Honourable Minister Prof. M.G.K. Menoninaugurates the conference Academic Programme List of Participants CONTENTS Functions of Generalized Bounded Argument Rotation 1 Introduction 2. Preliminaries 3. Functions of bounded argwnent rotation 4. Mocanu convexity of Rk [A, B] and Vk [A, B] 5. Functions of generalized bounded argument rotation References Meromorphic Functions and Differential Subordination 1. Introduction 2. The class Sigma(n; a; h) 3. The Class C* (n; a, h) 4. The Class 'Sigma alpha (n; a, h) References An Extension of certain classes of Univalent Functions 1. Introduction 2. Preliminaries 3. Main Results References On Properties of Polynomials of Special Types References Differential Inequalities and Local Valency 1. Introduction References Classes of Functions defined by subordination 1. Introduction 2. Inclusion Properties 3. Behaviour under various operators References A Note on Univalent Functions with Negative Coefficients 1. Introduction References Distortion theorems for hyperbolically and spherically k-convex functions 1. Introduction 2.Examples 3. Converting hyperbolically k-convex functions into euclidean Convex functions 4. Distortion and growth theorems 5.Comments 6. Spherical k ·convexity References On Integral Transfonns of Jakubowski Functions References Diff (Circle) and the Teichmiiller Spaces : A Connection Via String Theory References A Generalized Class of Analytic Functions 1. Introduction 2. Some Preliminary Lemmas 3. Some basic results in M£' (a, ~' b, c, a> References On the Fekete-Szego problem for close-to-convex functions of order p 1. Introduction 2. Preliminary Results 3. Main Results References Study ofRuscheweyh Integral Operators on certain classes of Meromorphic Functions References First Order Differential Inequalities in the Complex Plane 1. Introduction 2. Preliminaries 3. Differential Inequalities 4. Integral Inequalities References A Generalization of a Theorem of W .B. Ford References On a Boundary Value Problem for Convex Univalent Functions. ll1 I. Introduction and statement of the results II. Proofs of Theorems 1 and 3 III. The Applications References Some Properties of Certain Multivalent Function 1. Introduction 2. Some Properties of the Class Sp (a) 3. A Subclass Fp, b (a.) 4. Generalization of Saitoh's Result References A Survey of some recent results in the Theory of Harmonic Univalent Functions 1. Introduction 2. The harmonic classes S_h and S^o. 3. Some basic differences between the classes SHandS. 4. Mapping Theorems and boundary behaviour 5. The classes of univalent harmonic mappings between canonical regions 6. Variational methods for HOPU functions 7. Application to minimal surfaces References Conjectures for univalent functions with negative coefficients 1. Introduction 2. The Family T 3. Positive Order References Some Inequalities for Starlike and Spiral-like Functions 1. Introduction and statement of results 2. Some Preliminary Results 3. Proof of Theorem 1 4. Proof of Theorem 2 5. Proof of Theorem 3 6. Proof of Theorem 4 7. Proof of Theorem E References Extreme Points and Support Points of Certain Class of Analytic Functions Introduction 1. Extreme Points 2. Support Points References Some Subclasses of k-Valent Meromorphic Functions 1. Introduction 2. The classes R (k, A, B) and lE (k, A, B) 3. The classes M* (k, A, B) and lMI* (k, A, B) References Bazilevic functions with logarithmic growth Introduction Known Results New Results COUNI'ER EXAMPLES SOME OPEN PROBLEMS References Certain Subclasses of Analytic Functions Introduction Main Results References Open Problems J.M. ANDERSON, U.K. R.W. BARNARD, U.S.A. T. BULBOACA, Romania G.P. KAPOOR, India V. KARUNAKARAN, India. S.S. MILLER, USA. S.OWA, Japan. M. OBRADOVIC, Yugoslavia. R. PARVATHAM, India S. PONNUSAMY, India. Prem SINGH, India. J. S'fANKIEWICZ, Poland. D.K. THOMAS, U.K.