rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Advances in Summability and Approximation Theory
  name:
    name part: Mohiuddine, S. A.
    role:
      role term: editor.
    role:
      role term: edt
    role:
      role term: http://id.loc.gov/vocabulary/relators/edt
  name:
    name part: Acar, Tuncer.
    role:
      role term: editor.
    role:
      role term: edt
    role:
      role term: http://id.loc.gov/vocabulary/relators/edt
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: si
    date issued: 2018
    edition: 1st ed. 2018.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIII, 241 p. 10 illus., 9 illus. in color. online resource.
  abstract: This book discusses the Tauberian conditions under which convergence follows from statistical summability, various linear positive operators, Urysohn-type nonlinear Bernstein operators and also presents the use of Banach sequence spaces in the theory of infinite systems of differential equations. It also includes the generalization of linear positive operators in post-quantum calculus, which is one of the currently active areas of research in approximation theory. Presenting original papers by internationally recognized authors, the book is of interest to a wide range of mathematicians whose research areas include summability and approximation theory. One of the most active areas of research in summability theory is the concept of statistical convergence, which is a generalization of the familiar and widely investigated concept of convergence of real and complex sequences, and it has been used in Fourier analysis, probability theory, approximation theory and in other branches of mathematics. The theory of approximation deals with how functions can best be approximated with simpler functions. In the study of approximation of functions by linear positive operators, Bernstein polynomials play a highly significant role due to their simple and useful structure. And, during the last few decades, different types of research have been dedicated to improving the rate of convergence and decreasing the error of approximation.
  table of contents: Chapter 1. A Survey for Paranormed Sequence Spaces Generated by Infinite Matrices -- Chapter 2. Tauberian Conditions under which Convergence Follows from Statistical Summability by Weighted Means -- Chapter 3. Applications of Fixed Point Theorems and General Convergence in Orthogonal Metric Spaces -- Chapter 4. Application of Measure of Noncompactness to the Infinite Systems of Second-Order Differential Equations in Banach Sequence Spaces c, lp and c0β -- Chapter 5. Infinite Systems of Differential Equations in Banach Spaces Constructed by Fibonacci Numbers -- Chapter 6. Convergence Properties of Genuine Bernstein-Durrmeyer Operators -- Chapter 7. Bivariate Szasz Type Operators Based on Multiple Appell Polynomials -- Chapter 8. Approximation Properties of Chlodowsky Variant of (P, Q) SzAsz-Mirakyan-Stancu Operators -- Chapter 9. Approximation Theorems for Positive Linear Operators Associated with Hermite and Laguerre Polynomials -- Chapter 10. On Generalized Picard Integral Operators -- Chapter 11. From Uniform to Statistical Convergence of Binomial-Type Operators -- Chapter 12. Weighted Statistically Uniform Convergence of Bögel Continuous Functions by Positive Linear Operators -- Chapter 13. Optimal Linear Approximation under General Statistical Convergence -- Chapter 14. Statistical Deferred Cesaro Summability Mean Based on (p, q)-Integers with Application to Approximation Theorems -- Chapter 15. Approximation Results for an Urysohn-type Nonlinear Bernstein Operators.
  note: edited by S. A. Mohiuddine, Tuncer Acar.
  subject:
    topic: Sequences (Mathematics)
  subject:
    topic: Approximation theory
  subject:
    topic: Functional analysis
  subject:
    topic: Sequences, Series, Summability
  subject:
    topic: Approximations and Expansions
  subject:
    topic: Functional Analysis
  classification: QA292
  classification: QA295
  classification: 515.24
  related item:
    title info:
      title: Springer eBooks
  identifier: 9789811330773
  identifier: https://doi.org/10.1007/978-981-13-3077-3
  record info:
    record creation date: 181230
    record change date: 20191026171915.0
    record identifier: 978-981-13-3077-3