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Korovkin-type theorems in weighted Lp-spaces via summation process
1Kırıkkale University, Faculty of Science and Arts, Department of Mathematics, Yahşihan, Kırıkkale, Turkey.
Thescientificworldjournal
|December 6, 2013
Summary
This study extends Korovkin-type theorems for positive linear operators to weighted Lp spaces. It introduces A-summability as a stronger convergence method for approximation theory.
Area of Science:
- Approximation Theory
- Functional Analysis
Background:
- Korovkin-type theorems are fundamental for understanding uniform convergence of positive linear operators.
- Weighted Lp spaces (1 ≤ p < ∞) are crucial in modern analysis for both univariate and multivariate functions.
Purpose of the Study:
- To extend the applicability of Korovkin-type theorems to weighted Lp spaces.
- To investigate approximation properties using a stronger convergence concept.
Main Methods:
- Discussion of Korovkin-type theorems on weighted Lp spaces.
- Application of A-summability as a convergence method.
Main Results:
- Established Korovkin-type approximation theorems for positive linear operators in weighted Lp spaces.
- Demonstrated the effectiveness of A-summability in achieving stronger convergence results.
Conclusions:
- The findings generalize existing approximation theory results to a broader class of function spaces.
- A-summability offers a more powerful tool for analyzing operator convergence in approximation theory.
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