Applied Summability Methods

M. Mursaleen

ISBN 10: 331904608X / ISBN 13: 9783319046082

Editore: Springer International Publishing, Springer International Publishing Apr 2014, 2014

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Neuware -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 coreitems 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, andanalytic 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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 136 pp. Englisch.

Codice articolo 9783319046082

Dati bibliografici

• Titolo: Applied Summability Methods
• Editore: Springer International Publishing, Springer International Publishing Apr 2014
• Data di pubblicazione: 2014
• Lingua: Inglese
• ISBN 10: 331904608X
• ISBN 13: 9783319046082
• Rilegatura: Taschenbuch
• Condizione: Neu

Descrizione articolo

Riassunto

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.

Contenuti

Toeplitz Matrices.- Lambert Summability and the Prime Number Theorem.- Summability Tests for Singular Points.- Lototski Summability and Analytic Continuation.- Summability Methods for Random Variables.- Almost Summability.- Almost Summability of Taylor Series.- Matrix Summability of Fourier and Walsh-Fourier Series.- Almost Convergence in Approximation Process.- Statistical Summability.- Statistical Approximation.- Applications to fixed point theorems.- Bibliography.- Index.