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Matrix transformations between certain sequence spaces over the non-Newtonian complex field.

Uğur Kadak1, Hakan Efe2

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This study explores matrix transformations in sequence spaces using non-Newtonian calculus. It establishes conditions for matrix operators and introduces summability methods.

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Area of Science:

  • Analysis
  • Functional Analysis
  • Sequence Space Theory

Background:

  • Infinite matrices are general linear operators between sequence spaces.
  • Matrix transformations are crucial in sequence space analysis.
  • Non-Newtonian calculus offers a novel framework for mathematical analysis.

Purpose of the Study:

  • To introduce and analyze matrix transformations within sequence spaces over the field ℂ(*).
  • To characterize specific classes of infinite matrices using non-Newtonian calculus.
  • To establish necessary and sufficient conditions for matrix transformations between classical sets in ℂ(*).
  • To extend the concepts of sequence-to-sequence and series-to-series summability.

Main Methods:

  • Utilizing the framework of non-Newtonian calculus.
  • Applying principles of linear operator theory.
  • Defining and analyzing infinite matrices over the field ℂ(*).
  • Developing criteria for matrix transformations between sequence spaces.

Main Results:

  • Characterization of infinite matrices under non-Newtonian calculus.
  • Determination of conditions for transforming classical sequence sets.
  • Introduction of novel summability methods (sequence-to-sequence and series-to-series).

Conclusions:

  • The study provides a comprehensive framework for matrix transformations in ℂ(*) sequence spaces.
  • Non-Newtonian calculus offers new perspectives on matrix analysis and summability.
  • The findings contribute to the theoretical understanding of sequence spaces and their operators.