scholarly journals λ-double statistical convergence of functions

Filomat ◽  
2019 ◽  
Vol 33 (2) ◽  
pp. 519-524 ◽  
Author(s):  
Rabia Savaş
Keyword(s):  
Statistical Convergence ◽  
Strong Summability ◽  
Functions Of Two Variables ◽  
Measurable Functions

In this paper, the definitions of ?-double strong summability and ?-double statistical convergence for real valued measurable functions of two variables defined on (1,?)x(1,?) are presented. Using these definitions we present a series of basic results. Additionally, inclusion theorems, extension of existing results in the literature, and their variations have been established.

scholarly journals Sliding window convergence and lacunary statistical convergence for measurable functions via modulus function

2018 ◽  
Vol 36 (1) ◽  
pp. 161 ◽  
Author(s):  
Mohammad Mursaleen ◽  
Kuldip Raj
Keyword(s):  
Statistical Convergence ◽  
Sliding Window ◽  
Modulus Function ◽  
Convergence Criterion ◽  
Sequential Methods ◽  
Measurable Functions ◽  
Lacunary Statistical Convergence

In this paper we study the concepts of sliding window convergence for real valued measurable functions dened on [0,1) via modulus function. We also establish some inclusions and consistency theorems for sequential methods along with examples. Finally, we give a Cauchy convergence criterion.

scholarly journals Lacunary Statistical Convergence in Measure for Double Sequences of Fuzzy Valued Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Ömer Kişi
Keyword(s):  
Statistical Convergence ◽  
Double Sequence ◽  
Finite Measure ◽  
Measurable Space ◽  
Double Sequences ◽  
Convergence In Measure ◽  
Measurable Functions ◽  
Lacunary Statistical Convergence ◽  
Convergence Of Sequences ◽  
Sequences Of Fuzzy Numbers

Based on the concept of lacunary statistical convergence of sequences of fuzzy numbers, the lacunary statistical convergence, uniformly lacunary statistical convergence, and equi-lacunary statistical convergence of double sequences of fuzzy-valued functions are defined and investigated in this paper. The relationship among lacunary statistical convergence, uniformly lacunary statistical convergence, equi-lacunary statistical convergence of double sequences of fuzzy-valued functions, and their representations of sequences of α -level cuts are discussed. In addition, we obtain the lacunary statistical form of Egorov’s theorem for double sequences of fuzzy-valued measurable functions in a finite measurable space. Finally, the lacunary statistical convergence in measure for double sequences of fuzzy-valued measurable functions is examined, and it is proved that the inner and outer lacunary statistical convergence in measure are equivalent in a finite measure set for a double sequence of fuzzy-valued measurable functions.

scholarly journals Comparison of strong and statistical convergences in some families of summability methods

Filomat ◽  
2014 ◽  
Vol 28 (6) ◽  
pp. 1225-1236
Author(s):  
Anna Seletski ◽  
Anne Tali
Keyword(s):  
Strong Convergence ◽  
Statistical Convergence ◽  
Strong Summability ◽  
Convexity Theorem ◽  
Summability Methods

The paper deals with certain families {A?}(?>?0) of summability methods. Strong and statistical convergences in Ces?ro- and Euler-Knopp-type families {A?} are investigated. Convergence of a sequence x = (xn) with respect to the different strong summability methods [A?+1]t (with positive exponents t = (tn)) in a family {A?} is compared, and characterized with the help of statistical convergence. A convexity theorem for comparison of three strong summability methods [A?+1]t, [A?+1]t and [A?+1]t (? > ? > ? > ?0) in a Ces?ro-type family {A?} is proved. This theorem can be seen as a generalization of some convexity theorems known earlier. Interrelations between strong convergence and certain statistical convergence are also studied and described with the help of theorems proved here. All the results can be applied to the families of generalized N?rlund methods (N, p?n, qn).

scholarly journals Generalized Weighted Statistical Convergence for Double Sequences of Fuzzy Numbers and Associated Korovkin-Type Approximation Theorem

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Abdullah Alotaibi
Keyword(s):  
Statistical Convergence ◽  
Fuzzy Numbers ◽  
Approximation Theorem ◽  
Bernstein Operators ◽  
Double Sequences ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation ◽  
Functions Of Two Variables ◽  
Sequences Of Fuzzy Numbers ◽  
Bivariate Functions

We define the notions of weighted λ,μ-statistical convergence of order γ1,γ2 and strongly weighted λ,μ-summability of γ1,γ2 for fuzzy double sequences, where 0<γ1,γ2≤1. We establish an inclusion result and a theorem presenting a connection between these concepts. Moreover, we apply our new concept of weighted λ,μ-statistical convergence of order γ1,γ2 to prove Korovkin-type approximation theorem for functions of two variables in a fuzzy sense. Finally, an illustrative example is provided with the help of q-analogue of fuzzy Bernstein operators for bivariate functions which shows the significance of our approximation theorem.

Statistical convergence in a locally convex space

1988 ◽  
Vol 104 (1) ◽  
pp. 141-145 ◽  
Author(s):  
I. J. Maddox
Keyword(s):  
Convex Space ◽  
Statistical Convergence ◽  
Present Note ◽  
Locally Convex Space ◽  
Strong Summability ◽  
Modulus Function ◽  
Local Convexity ◽  
Complex Sequences ◽  
Topological Linear ◽  
Locally Convex

The notion of statistical convergence was introduced by Fast[1] and has been investigated in a number of papers[2, 5, 6]. Recently, Fridy [2] has shown that k(xk–xk+l) = O(1) is a Tauberian condition for the statistical convergence of (xk). Existing work on statistical convergence appears to have been restricted to real or complex sequences, but in the present note we extend the idea to apply to sequences in any locally convex Hausdorif topological linear space. Also we obtain a representation of statistical convergence in terms of strong summability given by a modulus function, an idea recently introduced in Maddox [3, 4]. Moreover Fridy's Tauberian result is extended so as to apply to sequences of slow oscillation in a locally convex space, and we also examine the local convexity of w(f) spaces.

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 Statistical σ-convergence of double sequences with application

Filomat ◽  
2018 ◽  
Vol 32 (8) ◽  
pp. 2783-2792
Author(s):  
M. Mursaleen ◽  
Cemal Belen ◽  
Syed Rizvi
Keyword(s):  
Statistical Convergence ◽  
Approximation Theorem ◽  
Invariant Mean ◽  
Double Sequences ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation ◽  
Functions Of Two Variables

The concepts of ?-statistical convergence, statistical ?-convergence and strong ?q-convergence of single (ordinary) sequences have been introduced and studied in [M. Mursaleen, O.H.H. Edely, On the invariant mean and statistical convergence, App. Math. Lett. 22, (2011), 1700-1704] which were obtained by unifying the notions of density and invariant mean. In this paper, we extend these ideas from single to double sequences. We also use the concept of statistical ?-convergence of double sequences to prove a Korovkin-type approximation theorem for functions of two variables and give an example to show that our Korovkin-type approximation theorem is stronger than those proved earlier by other authors.

scholarly journals On Generalized Statistical Convergence of Order of Difference Sequences

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Mikail Et ◽  
Hıfsı Altınok ◽  
Yavuz Altın
Keyword(s):  
Statistical Convergence ◽  
Strong Summability ◽  
Difference Sequences

We introduce the concept of statistical convergence of order of difference sequences, and we give some relations between the set of statistical convergence of order of difference sequences and strong -summability of order . Furthermore some relations between the spaces and are examined.

scholarly journals Statistical Approximation for Periodic Functions of Two Variables

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Abdullah Alotaibi ◽  
M. Mursaleen ◽  
S. A. Mohiuddine
Keyword(s):  
Statistical Convergence ◽  
Approximation Theorem ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Statistical Approximation ◽  
Periodic Functions ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation ◽  
Functions Of Two Variables ◽  
Function Of Two Variables

We prove a Korovkin type approximation theorem for a function of two variables by using the notion of statistical summability(C,1,1). We also study the rate of statistical summability(C,1,1)of positive linear operators. Finally we construct an example to show that our result is stronger than those previously proved for Pringsheim's convergence and statistical convergence.

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