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The unit step sequence is defined as 1 for zero and positive values of the integer n. This sequence can be graphically displayed using a set of eight sample points, showing a step function starting from n=0 and remaining constant thereafter.
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Generating Strictly Controlled Stimuli for Figure Recognition Experiments
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On generalized difference Hahn sequence spaces.

Kuldip Raj1, Adem Kiliçman2

  • 1School of Mathematics, Shri Mata Vaishno Devi University, Katra 182320, India.

Thescientificworldjournal
|July 16, 2014
PubMed
Summary

This study introduces generalized difference Hahn sequence spaces using modulus functions. Researchers investigated their topological properties, inclusion relations, dual spaces, and matrix transformations.

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Area of Science:

  • Mathematical Analysis
  • Sequence Space Theory

Background:

  • Sequence spaces are fundamental in functional analysis.
  • Generalized difference sequence spaces extend classical spaces with enhanced properties.

Purpose of the Study:

  • To construct and analyze novel generalized difference Hahn sequence spaces.
  • To investigate the topological characteristics and inclusion properties of these spaces.
  • To determine the dual spaces and characterize matrix transformations within this new framework.

Main Methods:

  • Construction of generalized difference Hahn sequence spaces using a sequence of modulus functions.
  • Application of topological analysis techniques.
  • Investigation of set-theoretic inclusion relations.
  • Computation of the dual spaces (preduals and duals).
  • Characterization of matrix transformations acting on these spaces.

Main Results:

  • Successfully constructed generalized difference Hahn sequence spaces denoted as h p ((F, u, Δ(r)).
  • Established key topological properties, including completeness and metrizability.
  • Determined the inclusion relations between different constructed spaces.
  • Computed the dual spaces, providing insights into their linear topological structure.
  • Characterized specific classes of matrix transformations, such as bounded and convergent transformations.

Conclusions:

  • The constructed generalized difference Hahn sequence spaces exhibit rich topological structures.
  • The findings contribute to the understanding of generalized sequence spaces and their properties.
  • The characterization of matrix transformations offers potential applications in approximation theory and summability.