On I-lacunary statistical convergence of weight g of sequences of sets

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5315-5322 ◽  
Author(s):  
Ekrem Savaş
Keyword(s):  
Statistical Convergence ◽  
Open Problems ◽  
New Approach ◽  
Summability Methods ◽  
Lacunary Statistical Convergence

In this paper, following a very recent and new approach of [1], we further generalize recently introduced summability methods in [13] and introduce new notions, namely, I-statistical convergence of weight 1 and I-lacunary statistical convergence of weight g, where g : N ? [0,?) is a function satisfying lim n?? g(n) = ? and n/g(n) ?? 0 as n ? ?, for sequences of sets. We mainly investigate their relationship and also make some observations about these classes. The study leaves a lot of interesting open problems.

scholarly journals I-lacunary summability function of order α

Filomat ◽  
2017 ◽  
Vol 31 (1) ◽  
pp. 69-76
Author(s):  
Ekrem Savaş
Keyword(s):  
Measurable Function ◽  
Statistical Convergence ◽  
Open Problems ◽  
Summability Methods

In this paper, we further generalize recently introduced summability methods in [23](where ideals of N were used to extend certain important summability methods) and introduce new notions, namely, I-statistical convergence of order ?, where 0 < ? < 1 by taking nonnegative real-valued Lebesque measurable function in the interval (1,?). We mainly investigate their relationship and also make some observations about these classes. The study leaves a lot of interesting open problems

scholarly journals I2-lacunary strongly summability for multidimensional measurable functions

2020 ◽  
Vol 107 (121) ◽  
pp. 93-107
Author(s):  
Rabia Savaş ◽  
Richard Patterson
Keyword(s):  
Statistical Convergence ◽  
New Approach ◽  
New Methods ◽  
Measurable Functions ◽  
Lacunary Statistical Convergence ◽  
Nontrivial Ideal

Let I2 ? P(N ? N) be a nontrivial ideal. We provide a new approach to the concept of I2-double lacunary statistical convergence and I2-lacunary strongly double summable by taking f(?,?), which is a multidimensional measurable real valued function on (1,?) ? (1,?). Additionally, we examine the relation between these two new methods.

scholarly journals On Some Further Generalizations of Strong Convergence in Probabilistic Metric Spaces Using Ideals

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Pratulananda Das ◽  
Kaustubh Dutta ◽  
Vatan Karakaya ◽  
Sanjoy Ghosal
Keyword(s):  
Strong Convergence ◽  
Metric Space ◽  
Statistical Convergence ◽  
Metric Spaces ◽  
Strong Topology ◽  
Probabilistic Metric Space ◽  
Probabilistic Metric Spaces ◽  
New Approach ◽  
Lacunary Statistical Convergence ◽  
Probabilistic Metric

Following the line of (Das et al., 2011, Savas and Das, 2011), we make a new approach in this paper to extend the notion of strong convergence and more general strong statistical convergence (Şençimen and Pehlivan, 2008) using ideals and introduce the notion of strongℐ- andℐ*-statistical convergence and two related concepts, namely, strongℐ-lacunary statistical convergence and strongℐ-λ-statistical convergence in a probabilistic metric space endowed with strong topology. We mainly investigate their interrelationship and study some of their important properties.

scholarly journals Orlicz–Pettis Theorem through Summability Methods

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 895 ◽  
Author(s):  
Fernando León-Saavedra ◽  
María del Pilar Romero de la Rosa ◽  
Antonio Sala
Keyword(s):  
Statistical Convergence ◽  
Summability Method ◽  
Matrix Summability ◽  
Summability Methods

This paper unifies several versions of the Orlicz–Pettis theorem that incorporate summability methods. We show that a series is unconditionally convergent if and only if the series is weakly subseries convergent with respect to a regular linear summability method. This includes results using matrix summability, statistical convergence with respect to an ideal, and other variations of summability methods.

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