The approximation of a continuous function by either an algebraic polynomial, a trigonometric polynomial, or a spline, is an important issue in application areas like computer-aided geometric design and signal analysis. This book is an introduction to the mathematical analysis of such approximation, and, with the prerequisites of only calculus and linear algebra, the material is targeted at senior undergraduate level, with a treatment that is both rigorous and self-contained. The topics include polynomial interpolation; Bernstein polynomials and the Weierstrass theorem; best approximations...

For more than a century, the study of various types of inequalities has been the focus of great attention by many researchers, interested both in the theory and its applications. The present monograph is an attempt to organize recent progress related to the above inequalities, which we hope will widen the scope of their applications.

The space C(X) of all continuous functions on a compact space X carries the structure of a normed vector space, an algebra and a lattice.

The chapters are "The origin of generalized metric spaces", "Mappings on metric spaces" and "Classes of generalized metric spaces".