Mathematical Inequalities

This book provides a comprehensive overview of mathematical inequalities, highlighting their significance and applications in various fields, including scientific modeling.

Drawing on a decade of research, Mathematical Inequalities offers an insightful perspective on the significance of various mathematical inequalities in modern mathematics. The authors explore how these inequalities are applied in diverse fields, including scientific modeling, highlighting their relevance in both theoretical and practical contexts. They present a thorough examination of classical and contemporary results that are accessible to both experts and those with a general scientific background.

Throughout the book, key inequalities involving real and complex numbers, as well as sequences in analysis, are meticulously described. Among the inequalities discussed are the Abel, Cauchy–Bunyakovsky–Schwarz, and De Bruijn’s inequalities. The authors also delve into integral inequalities, such as the Hermite–Hadamard inequalities, emphasizing their importance in modern analytical approaches. Additionally, the text covers a wide range of other inequalities, including those attributed to Bessel, Boas–Bellman, and Dunkl–William, along with their generalizations for isotonic linear and sublinear functionals.

Each inequality is accompanied by unique remarks that reveal the intricate connections between them. These discussions not only enhance the reader's understanding but also pave the way for future research in various applications and related fields. Mathematical Inequalities serves as a valuable resource for anyone interested in the profound implications of inequalities in mathematics and beyond.