Deferred Nörlund statistical convergence in probability, mean and distribution for sequences of random variables
Authors
K. Raj
 School of Mathematics, Shri Mata Vaishno Devi University, Katra182320, J \(\&\) K, India.
S. Jasrotia
 School of Mathematics, Shri Mata Vaishno Devi University, Katra182320, J \(\&\) K, India.
Abstract
We introduce and study deferred Nörlund statistical convergence in probability, mean of order \(r\), distribution and study the interrelation among them. Based upon the proposed method to illustrate the findings, we present new Korovkintype theorems for the sequence of random variables via deferred Nörlund statistically convergence and present compelling examples to demonstrate the effectiveness of the results.
Share and Cite
ISRP Style
K. Raj, S. Jasrotia, Deferred Nörlund statistical convergence in probability, mean and distribution for sequences of random variables, Journal of Nonlinear Sciences and Applications, 16 (2023), no. 1, 4150
AMA Style
Raj K., Jasrotia S., Deferred Nörlund statistical convergence in probability, mean and distribution for sequences of random variables. J. Nonlinear Sci. Appl. (2023); 16(1):4150
Chicago/Turabian Style
Raj, K., Jasrotia, S.. "Deferred Nörlund statistical convergence in probability, mean and distribution for sequences of random variables." Journal of Nonlinear Sciences and Applications, 16, no. 1 (2023): 4150
Keywords
 Probability convergence
 Deferred Nörlund
 Mean convergence
 Distribution convergence
 Statistical convergence
MSC
References

[1]
A. Altin, O. Doˇgru and F. Tas¸delen, The generalization of MeyerK¨onig and Zeller operators by generating functions, J. Math. Anal. Appl., 312 (2005), 181–194

[2]
H. Dutta, S. K. Paikray and B. B. Jena, On statistical deferred Ces`aro summability, Current Trends in Mathematical Analysis and Its Interdisciplinary Applications. Birkh¨auser, Cham, 487 (2019), 885909

[3]
A. Esi and E. Savas, On lacunary statistically convergent triple sequences in probabilistic normed space, Appl. Math. Inf. Sci., 9 (2015), 25292534

[4]
M. Et, P. Baliarsingh and H. Sengul, Deferred statistical convergence and strongly deferred summable functions, AIP Conf. Proc., 2183 (2019),

[5]
D. Eunice Jemima, V. Srinivasan, Norlund statistical convergence and Tauberian conditions for statistical convergence from statistical summability using Norlund means in nonArchimedean fields, Journal of Mathematics and Computer Science, 24 (2022), 299–307

[6]
H. Fast, Sur la convergence statistique, Colloquium Mathematicae, 2 (1951), 241244

[7]
J. A. Fridy, On statistical convergence, Analysis, 5 (1985), 301313

[8]
A. D. Gadjiev and C. Orhan, Some approximation theorems via statistical convergence, Rocky Mountain Journal of Mathematics, 32 (2002), 129138

[9]
S. Ghosal, Statistical convergence for a sequence of random variables and limit theorems, Appl. Math. (Prague), 58 (2013), 423437

[10]
B. Hazarika, N. Subramanian, and M. Mursaleen, Korovkintype approximation theorem for Bernstein operator of rough statistical convergence of triple sequences, Adv. Oper. Theory, 5 (2020), 324335

[11]
S. Jasrotia, U. P. Singh and K. Raj, Applications of Statistical Convergence of order (, + ) in difference sequence spaces of fuzzy numbers, J. Intell. Fuzzy Systems, 40 (2021), 46954703

[12]
B. B. Jena, S. K. Paikray and H. Dutta, On Various New Concepts of Statistical Convergence for Sequences of Random Variables via Deferred Ces`aro Mean, J. Math. Anal. Appl., 487 (2020),

[13]
V. A. Khan, H. Fatima, M. D. Khan, A. Ahamd, Spaces of neutrosophic statistical convergence sequences and their properties, Journal of Mathematics and Computer Science, 23 (2021), 1–9

[14]
S. A. Mohiuddine and B. A. S. Alamri, Generalization of equistatistical convergence via weighted lacunary sequence with associated Korovkin and Voronovskaya type approximation theorems, Rev. R. Acad. Cienc. Exactas F´ıs. Nat. Ser. A Mat. RACSAM, 113 (2019), 1955–1973

[15]
S. A. Mohiuddine, A. Alotaibi and M. Mursaleen, Statistical convergence of double sequences in locally solid Riesz spaces, Abstr. Appl. Anal., 2012 (2012),

[16]
S. A. Mohiuddine, A. Alotaibi, and M. Mursaleen, Statistical summability (C, 1) and a Korovkin type approximation theorem, J. Inequal. Appl., 2012 (2012), 18

[17]
M. Mursaleen, V. Karakaya, M. Ert ¨ urk and F G¨ ursoy, Weighted statistical convergence and its application to Korovkin type approximation theorem, Adv. Oper. Theory, 218 (2012), 91329137

[18]
M. Mursaleen, Applied Summability Methods, Springer Briefs. Springer, New York (2014)

[19]
K. Raj and A. Choudhary, Relative modular uniform approximation by means of the power series method with applications, Rev. Un. Mat. Argentina, 60 (2019), 187208

[20]
K. Raj and S. Pandoh, Some vectorvalued statistical convergent sequence spaces, Malaya J. Mat., 3 (2015), 161–167

[21]
D. Rath and B. C. Tripathy, Matrix maps on sequence spaces associated with sets of integers, Indian J. Pure Appl. Math., 27 (1996), 197206

[22]
I. J. Schoenberg, The integrability of certain functions and related summability methods, The American Mathematical Monthly, 66 (1959), 361775

[23]
H. M. Srivastava, B. B. Jena, S. K. Paikray and U. K. Misra, Generalized equistatistical convergence of the deferred N¨orlund summability and its applications to associated approximation theorems, Rev. R. Acad. Cienc. Exactas F´ıs. Nat. Ser. A Mat. RACSAM, 112 (2018), 1487–1501

[24]
H. M. Srivastava, B. B. Jena, S. K. Paikray, Statistical probability convergence via the deferred N¨orlund mean and its applications to approximation theorems, Rev. R. Acad. Cienc. Exactas F´ıs. Nat. Ser. A Mat. RACSAM, 114 (2020), 1 14

[25]
H. M. Srivastava, B. B. Jena, S. K. Paikray, Deferred Ces`aro statistical probability convergence and its applications to approximation theorems, J. Nonlinear Convex Anal., 20 (2019), 1777–1792

[26]
H. M. Srivastava, B. B. Jena and S. K. Paikray, A certain class of statistical probability convergence and its applications to approximation theorems, Appl. Anal. Discrete Math., 14 (2020), 579598

[27]
B.C. Tripathy, A. Esi and T. Balakrushna, On a new type of generalized difference Ces`aro sequence spaces, Soochow J. Math., 31 (2005), 333340.