On various new concepts of statistical convergence for sequences of random variables via deferred Cesàro mean

Jena, Bidu Bhusan; Dutta, Hemen

doi:10.1016/j.jmaa.2020.123950

Cited by 28 publications

(23 citation statements)

References 13 publications

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“…Finally, for the conditions (i) and (ii) (of Theorem 2) along with Lemma 2, the last inequality (22) helps us to achieve the assertion (21). Therefore, proof of Theorem 2 is completed.…”

Section: Fuzzy Rate Of Relatively Eqiu-statistical Convergencementioning

confidence: 79%

“…In the current years, the use of statistical convergence in approximation theory has enabled the researchers to achieve more powerful outcomes than that of the classical aspects of convergence. In this context, we refer to the recent works [9], [10], [15], [14], [13], [20], [21], [24], [22], [23], [25], [33], [34], [35], [36], [37], [38] and [40].…”

Section: Introductionmentioning

confidence: 99%

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A Certain Class of Relatively Equi-Statistical Fuzzy Approximation Theorems

Paikray¹,

Parida²,

Mohiuddine³

2020

Eur. J. Pure Appl. Math.

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The aim of this paper is to introduce the notions of relatively deferred Nörlund uniform statistical convergence as well as relatively deferred Norlund point-wise statistical convergence through the dierence operator of fractional order of fuzzy-number-valued sequence of functions, and a type of convergence which lies between aforesaid notions, namely, relatively deferred Nörlund equi-statistical convergence. Also, we investigate the inclusion relations among these aforesaidnotions. As an application point of view, we establish a fuzzy approximation (Korovkin-type) theorem by using our new notion of relatively deferred Norlund equi-statistical convergence and intimate that this result is a non-trivial generalization of several well-established fuzzy Korovkin-type theorems which were presented in earlier works. Moreover, we estimate the fuzzy rate of the relatively deferred Nörlund equi-statistical convergence involving a non-zero scale function by using the fuzzy modulus of continuity.

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“…Finally, for the conditions (i) and (ii) (of Theorem 2) along with Lemma 2, the last inequality (22) helps us to achieve the assertion (21). Therefore, proof of Theorem 2 is completed.…”

Section: Fuzzy Rate Of Relatively Eqiu-statistical Convergencementioning

confidence: 79%

Section: Introductionmentioning

confidence: 99%

A Certain Class of Relatively Equi-Statistical Fuzzy Approximation Theorems

Paikray¹,

Parida²,

Mohiuddine³

2020

Eur. J. Pure Appl. Math.

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“…Also, the statistical convergene and statistical summability are more general than the ordinary convergene and ordinary summability. For recent works in this direction, see [1], [5], [6], [8], [9], [10], [11], [15], [16], [17], [18], [19] and [20]. Dealing with strong summability of Nörlund mean Mittal [13] has proved a theorem as follows.…”

Section: Preliminariesmentioning

confidence: 99%

Strong Riesz summability of Fourier series

Jena

Misra

2020

Proyecciones (Antofagasta)

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“…Also, Das et al [2] used statistical (C, 1)(E, µ) product summability mean for sequences of fuzzy numbers to prove a fuzzy Korovkin-type approximation theorem. For more studies in this direction one may refer to [3], [4], [5], [7], [8], [14], [15] and [16]. Motivated essentially by the above mentioned works, we investigate here the characterization of generalized Nörlund and Nörlund-type (Riesz) means of sequences of fuzzy real numbers.…”

Section: Let Us Considermentioning

confidence: 99%

Generalized NÃ¶rlund and NÃ¶rlund-type Means of Sequences of Fuzzy Numbers

Pattanaik¹,

Paikray²,

Jena³

2020

Eur. J. Pure Appl. Math.

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In this article we study some properties of generalized Nörlund and Nörlund-typemeans of sequences of fuzzy real numbers. We establish necessary and sufficient conditions for our purposed methods to transform convergent sequences of fuzzy real numbers into convergent sequences of fuzzy real numbers which also preserve the limit. Finally, we establish some results showing the connection between the generalized N ̈orlund and N ̈orlund-type limits and the usual limits under slow oscillation of sequences of fuzzy real numbers.

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On various new concepts of statistical convergence for sequences of random variables via deferred Cesàro mean

Cited by 28 publications

References 13 publications

A Certain Class of Relatively Equi-Statistical Fuzzy Approximation Theorems

A Certain Class of Relatively Equi-Statistical Fuzzy Approximation Theorems

Strong Riesz summability of Fourier series

Generalized NÃ¶rlund and NÃ¶rlund-type Means of Sequences of Fuzzy Numbers

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