This book explores advanced topics in Geometric Function Theory and Complex Analysis, with a focus on analytic functions, differential operators, and their geometric properties. It draws from the rich tradition of the Romanian Mathematical School and highlights foundational results, contemporary research, and novel methods involving fractional calculus, q-calculus, and fuzzy analysis.Readers will find comprehensive coverage of: Classical and modern differential subordinations and superordinations;Strong and fuzzy differential operators;Key differential and integral operators, including q-analogues of well-known transformations;Applications of operators in defining new subclasses of analytic functions and analyzing their geometric features: starlikeness, convexity, distortion bounds, and more;The book builds on pioneering work by S S Miller, P T Mocanu, H M Srivastava, and others, offering new theoretical insights and practical tools for researchers in complex analysis and applied mathematics.Designed for graduate students, mathematics researchers, and theoretical physicists, this volume serves as both a reference and a research springboard for further study in geometric function theory, fractional and quantum calculus, and operator theory.

This book explores advanced topics in Geometric Function Theory and Complex Analysis, with a focus on analytic functions, differential operators, and their geometric properties. It draws from the rich tradition of the Romanian Mathematical School and highlights foundational results, contemporary research, and novel methods involving fractional calculus, q-calculus, and fuzzy analysis.Readers will find comprehensive coverage of: Classical and modern differential subordinations and superordinations;Strong and fuzzy differential operators;Key differential and integral operators, including q-analogues of well-known transformations;Applications of operators in defining new subclasses of analytic functions and analyzing their geometric features: starlikeness, convexity, distortion bounds, and more;The book builds on pioneering work by S S Miller, P T Mocanu, H M Srivastava, and others, offering new theoretical insights and practical tools for researchers in complex analysis and applied mathematics.Designed for graduate students, mathematics researchers, and theoretical physicists, this volume serves as both a reference and a research springboard for further study in geometric function theory, fractional and quantum calculus, and operator theory.