03675nam 22006735 450 991030015260332120200704224043.03-319-04609-810.1007/978-3-319-04609-9(CKB)3710000000094990(SSID)ssj0001186994(PQKBManifestationID)11787431(PQKBTitleCode)TC0001186994(PQKBWorkID)11243030(PQKB)11139918(MiAaPQ)EBC1697921(DE-He213)978-3-319-04609-9(PPN)177823038(EXLCZ)99371000000009499020140327d2014 u| 0engurcnu||||||||txtccrApplied Summability Methods /by M. Mursaleen1st ed. 2014.Cham :Springer International Publishing :Imprint: Springer,2014.1 online resource (129 pages) illustrations, tablesSpringerBriefs in Mathematics,2191-8198Bibliographic Level Mode of Issuance: Monograph3-319-04608-X Includes bibliographical references and index.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.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.SpringerBriefs in Mathematics,2191-8198Sequences (Mathematics)Number theoryMatrix theoryAlgebraSequences, Series, Summabilityhttps://scigraph.springernature.com/ontologies/product-market-codes/M1218XNumber Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M25001Linear and Multilinear Algebras, Matrix Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11094Sequences (Mathematics).Number theory.Matrix theory.Algebra.Sequences, Series, Summability.Number Theory.Linear and Multilinear Algebras, Matrix Theory.515.243Mursaleen Mauthttp://id.loc.gov/vocabulary/relators/aut1059247MiAaPQMiAaPQMiAaPQBOOK9910300152603321Applied Summability Methods2536255UNINA