Related Experiment Video
Updated: Jan 28, 2026
13:07
Convergent Polishing: A Simple, Rapid, Full Aperture Polishing Process of High Quality Optical Flats & Spheres
Published on: December 1, 2014
11.6K
Application of f-lacunary statistical convergence to approximation theorems
Vinod K Bhardwaj1, Shweta Dhawan2
11Department of Mathematics, Kurukshetra University, Kurukshetra, India.
Journal of Inequalities and Applications
|March 7, 2019
Summary
This study introduces f-lacunary statistical convergence, a new concept generalizing lacunary statistical convergence. Korovkin-type approximation theorems are established using this novel convergence method.
Area of Science:
- Mathematical Analysis
- Approximation Theory
Background:
- Lacunary statistical convergence is a known concept in mathematical analysis.
- The f-lacunary statistical convergence is a recent generalization of lacunary statistical convergence.
Purpose of the Study:
- To establish Korovkin-type approximation theorems utilizing the concept of f-lacunary statistical convergence.
- To explore the relationship between these new theorems and existing Korovkin theorems.
- To introduce and apply a new concept of f-lacunary statistical convergence of degree beta.
Main Methods:
- The study employs the definition of f-lacunary statistical convergence.
- Korovkin-type approximation theorems are proven using this framework.
- A new degree of f-lacunary statistical convergence is introduced.
Main Results:
- New Korovkin-type approximation theorems based on f-lacunary statistical convergence are established.
- The relationship between these new theorems and classical/lacunary statistical analogs is analyzed.
- A corresponding Korovkin-type theorem is derived for the newly introduced f-lacunary statistical convergence of degree beta.
Conclusions:
- The paper successfully extends Korovkin-type approximation theorems to the domain of f-lacunary statistical convergence.
- The findings provide new insights into approximation theory by incorporating generalized convergence concepts.
- The introduction of f-lacunary statistical convergence of degree beta opens avenues for further research in approximation theory.
Related Concept Videos
01:29Application of Linearization and Approximation
87
A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...
87
01:54Convergent Evolution
32.7K
Evolution shapes the features of organisms over time, ensuring that they are suited for the environments in which they live. Sometimes, selection pressure leads to the rise of similar but unrelated adaptations in organisms with no recent common ancestors, a process known as convergent evolution.
32.7K
01:50Statistical Significance
21.3K
Once data is collected from both the experimental and the control groups, a statistical analysis is conducted to find out if there are meaningful differences between the two groups. A statistical analysis determines how likely any difference found is due to chance (and thus not meaningful). In psychology, group differences are considered meaningful, or significant, if the odds that these differences occurred by chance alone are 5 percent or less. Stated another way, if we repeated this...
21.3K
01:26Linearization and Approximation
53
Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
53
01:28Accuracy, limits, and approximation
1.3K
Accuracy, limits, and approximations are common in many fields, especially in engineering calculations. These concepts are imperative for ensuring that a given value is as close as possible to its true value.
Accuracy is defined as the closeness of the measured value to the true or actual value. In engineering mechanics, repeated measurements are taken during theoretical or experimental analyses to ensure that the result is precise and accurate.
The accuracy of any solution is based on the...
Accuracy is defined as the closeness of the measured value to the true or actual value. In engineering mechanics, repeated measurements are taken during theoretical or experimental analyses to ensure that the result is precise and accurate.
The accuracy of any solution is based on the...
1.3K
01:17Region of Convergence
915
The z-transform is a powerful mathematical tool used in the analysis of discrete-time signals and systems. It is a crucial tool in the analysis of discrete-time systems, but its convergence is limited to specific values of the complex variable z. This range of values, known as the Region of Convergence (ROC), is fundamental in determining the behavior and stability of a system or signal. The ROC defines the region in the complex plane where the z-transform converges, which can take various...
915