Fix-Points and Factorization of Meromorphic Functions

The fix-points and factorization of meromorphic functions have become two research topics that have attracted many complex analysts' attention throughout the world; notably in U.S., China, and Japan. The first two chapters reintroduce Nevanlinna's theory of meromorphic functions and Montel's normal families theory for entire functions. Based on these, several theorems on fix-points were derived. The last two chapters introduce the factorization theory and the relationships between the fix-points and factorization; many recent results in factorization theory were reported and related open questions were raised for further study. This book provides a timely introduction to some of the topics that are currently pursued by many complex analysts. For instance, the fix-points of itrates of functions is closely related to the fractal mathematics, which has just been realized to be useful in many branches of engineering and physics as well as in computer graphics.

• Nevanlinna's Theory of Meromorphic Functions
• Fix-Points of Meromorphic Functions
• Factorization of Mermorphic Functions
• Fix-Points and Theory of Factorization
• Appendixes: Functional Identities
• Relations Between the Growths of f(g), f, and g
• The Extension of Polya's Theorem to Meromorphic Functions
• Some Necessary Conditions for the Existence of Meromorphic Solutions of Certain Differential Equations
• Some Properties of Differential Polynomials
• A Simpler Proof of Steinmetz's Theorem