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The Resource Current Topics in Summability Theory and Applications

Current Topics in Summability Theory and Applications

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Current Topics in Summability Theory and Applications
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Current Topics in Summability Theory and Applications
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eng
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MiAaPQ
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non fiction
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dictionaries
Current Topics in Summability Theory and Applications
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Current Topics in Summability Theory and Applications
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http://libproxy.rpi.edu/login?url=https://ebookcentral.proquest.com/lib/rpi/detail.action?docID=4516755
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online resource
Carrier category code
cr
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rdacarrier
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multicolored
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text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • Preface -- Contents -- Editors and Contributors -- An Introduction to Summability Methods -- 1 Introduction -- 2 Basic Technique -- 3 Basic Process -- 3.1 T-Process -- 3.2 Characterization of T-Process -- 3.3 Regularity Condition -- 3.4 Range Condition -- 3.5 Conservative Process -- 3.6 T-Summability -- 3.7 z-Processes -- 4 Particular Methods of Summability -- 4.1 Matrix Summability -- 4.2 Cesàro Summability -- 4.3 Hölder Summability -- 4.4 Harmonic Summability -- 4.5 Generalized Cesàro Summability -- 4.6 Riesz's Typical Means Summability -- 4.7 Nörlund Summability -- 4.8 Riesz Summability -- 4.9 Generalized Nörlund Summability -- 4.10 Indexed Summability Methods -- 4.11 Abel Summability -- 4.12 Euler Summability -- 4.13 Borel Summability -- 4.14 Hausdorff Summability -- 4.15 Banach Summability -- References -- Some Topics in Summability Theory -- 1 Weighted Mean Method -- 2 (M, nn) Method or Natarajan Method -- 3 The Natarajan Method and the Abel Method -- 4 The Euler Method and the Natarajan Method -- 5 Some More Nice Properties of the Natarajan Method -- 6 A Steinhaus Type Theorem -- 7 On the Sequence Space Nr -- 8 Core of a Sequence -- 9 The Matrix Class (ell, ell) -- References -- Summability and Convergence Using Ideals -- 1 Introduction -- 2 Ideal Convergence of Single Sequences -- 2.1 mathcalI-convergence, Examples, and Properties -- 2.2 mathcalI-convergence and mathcalI*-convergence -- 2.3 mathcalI-Limit Points and mathcalI-Cluster Points -- 2.4 Convergence Field of mathcalI-convergence -- 2.5 mathcalI-Cauchy Condition -- 3 Ideal Convergence of Double Sequences -- 3.1 Basic Ideas of mathcalI and mathcalI*-convergent Double Sequences -- 3.2 mathcalI-Variation of Double Sequences and the set W2(mathcalI) -- 4 Ideal Convergence of Nets -- 4.1 Basic Definitions and Properties of mathcalI-convergent Nets
  • 4.2 mathcalI*-convergence of Nets and the Condition (DP) -- 4.3 mathcalI-Cauchy Nets in a Uniform Space -- 5 Extension of mathcalI* Concept Using Two Ideals -- 5.1 Basic Ideas and Associated Results -- 5.2 mathcalImathcalJ-Cauchy Functions and Completeness -- 5.3 Condition AP(mathcalI,mathcalJ) -- 6 Certain Generalized Summability Methods Using Ideals -- 6.1 Basic Ideas and Results -- 6.2 On mathcalI-Statistically pre-Cauchy Sequences -- 7 Convergence of Sequences of Functions with Respect to Ideals -- References -- Convergence Acceleration and Improvement by Regular Matrices -- 1 Introduction -- 2 Convergence and Summability with Speed and Auxiliary Results -- 3 On o-Faster Convergence of Sequences -- 4 Weak and Strong o-Faster Convergence of Sequences -- 5 o-Acceleration of Convergence by Regular Matrices -- 6 Strong o-Acceleration of Convergence by Regular Matrices -- 7 Improvement of Convergence and n-Boundedness of Sequences -- 8 Improvement of Convergence and n-Boundedness by Sr-Sq Regular Matrices -- 9 Improvement of An-Boundedness Using Nontriangular Sr-Sq Regular Matrices -- 10 On Increasing the Order of Approximation of Fourier Expansions by Nontriangular Sr-Sq Regular Matrices -- References -- On Summability, Multipliability, and Integrability -- 1 Introduction -- 2 Summability -- 3 Integrability -- 3.1 Preliminaries -- 3.2 Integrability of Step Mappings -- 3.3 Integrability of Right Regulated Mappings -- 3.4 Applications to Impulsive Differential Equations -- 4 Multipliability -- 5 Product Integrability -- 5.1 Preliminaries -- 5.2 Product Integrability of Step Mappings -- 5.3 Product Integrability of Right Regulated Mappings -- 6 Distributions and Summability -- 6.1 Distributions and Their Primitives -- 6.2 The RD Primitive Integral and Its Basic Properties -- 6.3 On a Distributional Differential Equation -- References
  • Multi-dimensional Summability Theory and Continuous Wavelet Transform -- 1 Introduction -- 2 Wiener Amalgam Spaces -- 3 k-Summability of One-Dimensional Fourier Transforms -- 4 Circular k-Summability of Fourier Transforms -- 4.1 Norm Convergence of the k-Summability -- 4.2 Almost Everywhere Convergence of the k-Summability -- 4.3 Some Summability Methods -- 5 Rectangular k-Summability of Fourier Transforms -- 5.1 Norm Convergence of the k-Summability in Pringsheim's Sense -- 5.2 Almost Everywhere Convergence of the k-Summability in Pringsheim's Sense -- 5.3 Some Summability Methods -- 6 One-Dimensional Continuous Wavelet Transform -- 6.1 Orthogonality Results -- 6.2 Inversion Formulas -- 7 Convergence of the Multi-dimensional Inverse Wavelet Transform as Sto0,Ttoinfty, S,TinmathbbR+ -- 7.1 Multi-dimensional Continuous Wavelet Transform -- 7.2 Convergence of uS,Tf -- 7.3 Convergence of uSf -- 8 Convergence of the Multi-dimensional Inverse Wavelet Transform in Pringsheim's Sense, as Sto0,Ttoinfty, S,TinmathbbR+d -- 8.1 Multi-dimensional Continuous Wavelet Transform in the Pringsheim's Sense -- 8.2 Convergence of uS,Tf in Pringsheim's Sense -- 8.3 Convergence of uSf in Pringsheim's Sense -- References -- Absolute Riesz and Related Summability Methods -- 1 Introduction -- 2 On Generalized Absolute Cesàro Summability -- 3 On Quasi Monotone Sequences and Their Applications -- 4 Applications of Absolute Matrix Summability Using Almost Increasing Sequences -- 5 Generalized Absolute Matrix Summability -- 6 On Quasi Power Increasing Sequences -- 7 Generalized Absolute Riesz and Absolute Matrix Summability -- References -- Some Applications of Summability Theory -- 1 Introduction -- 2 Sequence Spaces -- 2.1 Cesro Convergence -- 2.2 Modular Functions -- 2.3 Relations Between Nk(A,F,u,Em) and Nk(A,u,Em)
  • 2.4 Lacunary (A,u,Em)-statistical Convergent Sequences -- 2.5 Cesro (A,u,Em)-convergent Sequences -- 2.6 Some Sequence Spaces Defined by Summability Methods and Lacunary Sequences -- 2.7 Results on Statistical Convergence -- 2.8 Some Geometric Properties of Sequence Spaces Defined by Summability Methods -- 2.9 Topological Properties -- 2.10 Geometrical Properties -- 2.11 New Sequence Spaces Defined by Summability Methods and Generalized Weighted Sequences -- 2.12 Notion of the n2-convergent Sequences -- 2.13 The Sequence Space l(n2,p) -- 2.14 Duals of the Space l(n2,p) -- 2.15 Some Matrix Transformations Related to the Sequence Space l(n2,p) -- 3 Tauberian Theorems -- 3.1 Tauberian Theorems Under the Generalized de la Valle-Poussin Mean -- 3.2 Tauberian Theorems Under Cn1Nnp Summability Method -- 3.3 Tauberian Theorems Under Nörlund-Cesáro Summability Method -- References -- Degree of Approximation of Functions Through Summability Methods -- 1 Introduction -- 2 Approximation of Functions by Almost Riesz Means -- 2.1 Definitions and Preliminaries -- 2.2 Results -- 2.3 Applications -- 3 Approximation of Functions by Euler (E,q) Mean -- 3.1 Known Results -- 3.2 Results -- 3.3 Corollaries -- 3.4 An Example -- References
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9789811009136
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rdamedia
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