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This book discusses recent developments in approximation theory and Fourier analysis, using different types of means such as delayed arithmetic mean and Deferred Cesaro mean. The theory of degree of approximation of functions by Fourier series provides various scientific applications in different branches of Science and Technology including partial differential equations, number theory, combinatorics, signal processing, cryptography, statistics, oceanography, optics, and many more. This book can be used as a textbook for graduate students, and as a valuable reference guide for young researchers in approximation theory.