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NON-NEWTONIAN SEQUENCE SPACES WITH APPLICATIONS.

Non-Newtonian Sequence Spaces with Applications presents an alternative to the usual calculus based on multiplication instead of addition. The book is intended for graduate students and researchers with a special interest in non-Newtonian calculus, its applications and related topics.Features Valuab...

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Bibliographic Details
Main Author: Başar, Feyzi
Corporate Author: Taylor & Francis
Other Authors: Hazarika, Bipan
Format: eBook
Language:English
Published: Boca Raton : CRC Press, Taylor & Francis Group, 2025.
Series:Monographs and research notes in mathematics.
Subjects:
Calculus.
Calcul infinitésimal.
calculus.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Cover
  • Half Title
  • Series Page
  • Title Page
  • Copyright Page
  • Dedication
  • Table of Contents
  • Preface
  • Acknowledgements
  • About the Authors
  • List of Abbreviations and Symbols
  • 1 Sequence and Function Spaces over the Non-Newtonian Fields
  • 1.1 Some Basic Results on the Spaces of Sequences with Geometric Calculus
  • 1.1.1 Preliminaries, Background, and Notation
  • 1.1.2 Geometric Complex Field and Related Properties
  • 1.1.3 Geometric Metric Spaces
  • 1.1.4 Convergence and Completeness in (GC)
  • 1.1.5 Sequence Spaces Over C(G)
  • 1.2 Some Results on Sequence Spaces with Respect to Non-Newtonian Calculus
  • 1.2.1 Preliminaries, Background, and Notations
  • 1.2.2 Non-Newtonian Real Field and Related Properties
  • 1.2.3 Non-Newtonian Metric Spaces
  • 1.2.4 Convergence and Completeness in (NC)
  • 1.3 Sequence Spaces over the Non-Newtonian Real Field
  • 1.4 Certain Non-Newtonian Complex Sequence Spaces
  • 1.4.1 Preliminaries, Background, and Notations
  • 1.5 Applications
  • 1.6 Some Sequence Spaces and Matrix Transformations in Multiplicative Sense
  • 1.6.1 Introduction
  • 1.6.2 Preliminaries, Background, and Notations
  • 2.6.1 Geometric Factorial
  • 2.6.2 Generalized Geometric Forward Difference Operator
  • 2.6.3 Generalized Geometric backward Difference Operator
  • 2.6.4 Factorial Function
  • 2.6.5 Geometric Newton-Gregory Forward Interpolation Formula
  • 2.6.6 Geometric Newton-Gregory Backward Interpolation Formula
  • 2.6.7 Advantages of Geometric Interpolation Formulae over Ordinary Interpolation Formulae
  • 2.7 Conclusion
  • 3 Bigeometric Calculus and Its Applications
  • 3.1 Introduction
  • 3.1.1 Some Useful Relations between Geometric Operations and Ordinary Arithmetic Operations