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Focuses exclusively on the study of summability methods and their applications
Features self-contained chapters appropriate for researchers and graduate students
Includes topics such as proof of the prime number theorem using Lambert's summability and Wiener's Tauberian theorem
This short monograph is the first book to focus exclusively on the study of summability methods, which have become active areas of research in recent years. The book provides basic definitions of sequence spaces, matrix transformations, regular matrices and some special matrices, making the material accessible to mathematicians who are new to the subject. Among the core items covered are the proof of the Prime Number Theorem using Lambert's summability and Wiener's Tauberian theorem, some results on summability tests for singular points of an analytic function, and analytic continuation through Lototski summability. Almost summability is introduced to prove Korovkin-type approximation theorems and the last chapters feature statistical summability, statistical approximation, and some applications of summability methods in fixed point theorems.
Content Level »Research
Keywords »Korovkin approximation theorems - Lambert summability - Lototski summability - Toeplitz matrices - prime number theorem - statistical approximation