LEADER 03675nam 22006735 450 001 9910300152603321 005 20200704224043.0 010 $a3-319-04609-8 024 7 $a10.1007/978-3-319-04609-9 035 $a(CKB)3710000000094990 035 $a(SSID)ssj0001186994 035 $a(PQKBManifestationID)11787431 035 $a(PQKBTitleCode)TC0001186994 035 $a(PQKBWorkID)11243030 035 $a(PQKB)11139918 035 $a(MiAaPQ)EBC1697921 035 $a(DE-He213)978-3-319-04609-9 035 $a(PPN)177823038 035 $a(EXLCZ)993710000000094990 100 $a20140327d2014 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aApplied Summability Methods /$fby M. Mursaleen 205 $a1st ed. 2014. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2014. 215 $a1 online resource (129 pages) $cillustrations, tables 225 1 $aSpringerBriefs in Mathematics,$x2191-8198 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-319-04608-X 320 $aIncludes bibliographical references and index. 327 $aToeplitz 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. 330 $aThis short monograph is the first book to focus exclusively on the study of summability methods, which have become active areas of research in recent years. The book provides basic definitions of sequence spaces, matrix transformations, regular matrices and some special matrices, making the material accessible to mathematicians who are new to the subject. Among the core items covered are the proof of the Prime Number Theorem using Lambert's summability and Wiener's Tauberian theorem, some results on summability tests for singular points of an analytic function, and analytic continuation through Lototski summability. Almost summability is introduced to prove Korovkin-type approximation theorems and the last chapters feature statistical summability, statistical approximation, and some applications of summability methods in fixed point theorems. 410 0$aSpringerBriefs in Mathematics,$x2191-8198 606 $aSequences (Mathematics) 606 $aNumber theory 606 $aMatrix theory 606 $aAlgebra 606 $aSequences, Series, Summability$3https://scigraph.springernature.com/ontologies/product-market-codes/M1218X 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 606 $aLinear and Multilinear Algebras, Matrix Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M11094 615 0$aSequences (Mathematics). 615 0$aNumber theory. 615 0$aMatrix theory. 615 0$aAlgebra. 615 14$aSequences, Series, Summability. 615 24$aNumber Theory. 615 24$aLinear and Multilinear Algebras, Matrix Theory. 676 $a515.243 700 $aMursaleen$b M$4aut$4http://id.loc.gov/vocabulary/relators/aut$01059247 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300152603321 996 $aApplied Summability Methods$92536255 997 $aUNINA