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This book focuses on some important classical parts of Geometry, Analysis and Number theory. The material is divided into ten chapters, including new advances on triangle or tetrahedral inequalities; special sequences and series of real numbers; various algebraic or analytic inequalities with applications; special functions(as Euler gamma and beta functions) and special means( as the logarithmic, identric, or Seiffert's mean); Arithmetic functions and arithmetic inequalities with connections to perfect numbers or related fields; and many more. The majority of the presented topics are based on...

This monograph is devoted to arithmetic functions, an area of number theory. Arithmetic functions are very important in many parts of theoretical and applied sciences, and many mathematicians have devoted great interest in this field. One of the interesting features of this book is the introduction and study of certain new arithmetic functions that have been considered by the authors separately or together, and their importance is shown in many connections with the classical arithmetic functions or in their applications to other problems.