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Binomial difference sequence spaces of fractional order.

Jian Meng1, Liquan Mei1

  • 1School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, P.R. China.

Journal of Inequalities and Applications
|October 27, 2018
PubMed
Summary
This summary is machine-generated.

This study introduces new sequence spaces and explores their fundamental properties and dual spaces. Researchers analyzed inclusion relations and various duals for these novel mathematical sets.

Keywords:
Fractional difference operatorMatrix transformationSequence spaceα-, β-, and γ-duals

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Area of Science:

  • Mathematics
  • Functional Analysis
  • Sequence Spaces

Background:

  • Sequence spaces are fundamental in mathematical analysis.
  • Understanding their properties is crucial for advanced mathematical research.
  • Existing literature provides a foundation for exploring new sequence spaces.

Purpose of the Study:

  • Introduce novel sequence spaces: , , and .
  • Investigate the functional properties of these new spaces.
  • Determine the inclusion relations and dual spaces (α-, β-, γ-, and continuous duals).

Main Methods:

  • Definition and construction of the new sequence spaces.
  • Application of standard functional analysis techniques.
  • Analysis of set inclusions and topological properties.
  • Computation of α-, β-, γ-, and continuous duals.

Main Results:

  • The paper defines and characterizes three new sequence spaces.
  • Key functional properties and inclusion relationships are established.
  • The α-, β-, γ-, and continuous duals of these spaces are determined.

Conclusions:

  • The introduction of these sequence spaces expands the landscape of mathematical analysis.
  • The detailed investigation provides a basis for future research in related areas.
  • The findings contribute to the understanding of topological vector spaces and their duals.