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The book provides a self-contained introduction to classical Number Theory. All the proofs of the individual theorems and the solutions of the exercises are being presented step by step. Some historical remarks are also presented. The book will be directed to advanced undergraduate, beginning graduate students as well as to students who prepare for mathematical competitions (ex. Mathematical Olympiads and Putnam Mathematical competition).

As Richard Bellman has so elegantly stated at the Second International Conference on General Inequalities (Oberwolfach, 1978), There are three reasons for the study of inequalities: practical, theoretical, and aesthetic. On the aesthetic aspects, he said, As has been pointed out, beauty is in the eye of the beholder. However, it is generally agreed that certain pieces of music, art, or mathematics are beautiful. There is an elegance to inequalities that makes them very attractive.

The content of the Handbook focuses mainly on both old and recent developments on approximate...

This handbook consists of seventeen chapters written by eminent scientists from the international mathematical community, who present important research works in the field of mathematical analysis and related subjects, particularly in the Ulam stability theory of functional equations. The book provides an insight into a large domain of research with emphasis to the discussion of several theories, methods and problems in approximation theory, analytic inequalities, functional analysis, computational algebra and applications.

The notion of stability of functional equations has its...

Important results surrounding the proof of Goldbach's ternary conjecture are presented in this book. Beginning with an historical perspective along with an overview of essential lemmas and theorems, this monograph moves on to a detailed proof of Vinogradov's theorem. The principles of the Hardy-Littlewood circle method are outlined and applied to Goldbach's ternary conjecture. New results due to H. Maier and the author on Vinogradov's theorem are proved under the assumption of the Riemann hypothesis. The final chapter discusses an approach to Goldbach's conjecture through...

The book provides a self-contained introduction to classical Number Theory. All the proofs of the individual theorems and the solutions of the exercises are being presented step by step. Some historical remarks are also presented. The book will be directed to advanced undergraduate, beginning graduate students as well as to students who prepare for mathematical competitions (ex. Mathematical Olympiads and Putnam Mathematical competition).

This contributed volume focuses on various important areas of mathematics in which approximation methods play an essential role. It features cutting-edge research on a wide spectrum of analytic inequalities with emphasis on differential and integral inequalities in the spirit of functional analysis, operator theory, nonlinear analysis, variational calculus, featuring a plethora of applications, making this work a valuable resource. The reader will be exposed to convexity theory, polynomial inequalities, extremal problems, prediction theory, fixed point theory for operators, PDEs,...