This book presents solutions to various extremal problems in analysis and provides mathematical tools that can be used to solve complex problems in different areas of fundamental and applied science.  These problems are not just theoretical, but they have practical applications in various fields including optimization and image processing.  The book includes an in-depth exploration of Ostrowski type inequalities, covering their applications to operator theory, inequalities for derivatives, and optimization of cubature formulae.  The authors also provide a comprehensive treatment of the Bojanov-Naidenov and Erdos problems and investigate their solutions for various function classes including differentiable functions, trigonometric polynomials, and splines. Additionally, the book explores sharp Remez type inequalities. These inequalities are examined in different metrics for various function classes including trigonometric polynomials and splines.  The authors also include innovative  research in image processing, focusing on the restoration of noise-corrupted optical images with simultaneous contrast enhancement and a variational approach to simultaneous fusion and denoising of color images with different spatial resolutions. This book is a valuable resource for researchers and graduate students in approximation theory, numerical analysis, and image processing.