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Novel Sequence Discovery by Subtractive Genomics
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Creating a novel algorithm for studying the strong convergence to a sequence with applications.

Hasanen A Hammad1, Mohammed E Dafaalla1, Manal Elzain Mohamed Abdalla2

  • 1Department of Mathematics, College of Sciences, Qassim University, Buraydah, Saudi Arabia.

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Summary

A new algorithm explores sequence convergence using generalized demimetric operators in Hilbert spaces. This method proves effective for solving complex optimization and feasibility problems.

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Area of Science:

  • Real Analysis
  • Operator Theory
  • Optimization

Background:

  • Investigating the convergence of sequences is crucial in various mathematical fields.
  • Existing operator theory has limitations in handling specific convergence conditions.

Purpose of the Study:

  • Introduce a novel algorithm for strong convergence analysis.
  • Extend operator theory with a finite family of generalized demimetric operators.
  • Apply the algorithm to split minimization and feasibility problems.

Main Methods:

  • Development of a new iterative algorithm.
  • Utilizing generalized demimetric operators within real Hilbert spaces.
  • Demonstrating convergence properties under specific conditions.

Main Results:

  • The proposed algorithm establishes strong convergence of sequences.
  • The framework successfully incorporates a finite family of generalized demimetric operators.
  • The algorithm's efficacy is shown in solving split minimization and feasibility problems.

Conclusions:

  • The novel algorithm provides an efficient tool for strong convergence analysis.
  • The research expands the scope of operator theory in Hilbert spaces.
  • The algorithm has significant potential in optimization and numerical analysis.