# Applications of statistical Riemann and Lebesgue integrability of sequence of functions

Volume 16, Issue 1, pp 30--40
Publication Date: March 17, 2023 Submission Date: December 23, 2022 Revision Date: March 01, 2023 Accteptance Date: March 05, 2023
• 22 Views

### Authors

K. Raj - School of Mathematics, Shri Mata Vaishno Devi University, Katra-182320, J $\&$ K, India. S. Sharma - School of Mathematics, Shri Mata Vaishno Devi University, Katra-182320, J $\&$ K, India.

### Abstract

In the present work, we propose to investigate statistical Riemann integrability, statistical Riemann summability, statistical Lebesgue integrability and statistical Lebesgue summability by means of deferred Nörlund and deferred Riesz mean. We discuss some fundamental theorems connecting these concepts with examples. As an application to our newly formed sequences, we introduce Korovkin-type approximation theorems with relevant example for positive linear operators by using Meyer-König and Zeller operators to exhibit the effectiveness of our findings.

### Share and Cite

##### ISRP Style

K. Raj, S. Sharma, Applications of statistical Riemann and Lebesgue integrability of sequence of functions, Journal of Nonlinear Sciences and Applications, 16 (2023), no. 1, 30--40

##### AMA Style

Raj K., Sharma S., Applications of statistical Riemann and Lebesgue integrability of sequence of functions. J. Nonlinear Sci. Appl. (2023); 16(1):30--40

##### Chicago/Turabian Style

Raj, K., Sharma, S.. "Applications of statistical Riemann and Lebesgue integrability of sequence of functions." Journal of Nonlinear Sciences and Applications, 16, no. 1 (2023): 30--40

### Keywords

• Statistical convergence
• Riemann integral
• Lebesgue integral
• deferred Riesz
• deferred Nörlund mean
• Korovkin-type approximation theorem

•  40A05
•  40A30
•  40G15