"Analytic Function Subfamilies: Univalent and Multivalent" written by S. Chandralekha is an extensive guide to the study of subfamilies of analytic functions, focusing on both univalent and multivalent functions. The book covers a broad range of topics related to complex analysis, including the properties of functions, geometric function theory, conformal mapping, and integral representation.
The author provides a comprehensive analysis of univalent function theory, multivalent function theory, coefficient bounds, starlike functions, convex functions, close-to-convex functions, sufficient conditions, and necessary conditions. The book also covers growth theory, singularities, special functions such as Bessel functions, hypergeometric functions, Painlevé transcendents, orthogonal polynomials, continued fractions, infinite products, q-series, generating functions, orthogonal functions, and symmetric functions.
The book delves into the study of complex variables, partial differential equations, harmonic analysis, Laplace equation, Cauchy-Riemann equations, function approximation, numerical methods, quadrature methods, Taylor series, Laurent series, convergence, holomorphic functions, meromorphic functions, and normal families.
The author provides clear and concise explanations of complex mathematical concepts and uses numerous examples and exercises to help readers develop their understanding of the subject. The book is an essential resource for researchers, graduate students, and academics in the field of mathematics and applied sciences who are interested in the study of subfamilies of analytic functions and their properties. It is also an excellent reference for anyone seeking a deeper understanding of complex analysis and its applications.
