Approximation Theory

The monograph explores the computational aspects of moduli of continuity for various functions, emphasizing convexity properties and presenting a comprehensive calculus of smoothness. It uniquely avoids the K-functional method to provide explicit error values in approximation theory. Part II delves into the Global Smoothness Preservation Property (GSPP) across numerous linear approximation operators, offering a general theory and diverse applications in mathematics and computer-aided geometric design. This work is notable for its thorough examination of GSPP and its integration with moduli of smoothness.