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Analysis, 1985
A sequence \(\{x_ k\}^{\infty}_{k=1}\) is said to be statistically convergent to \(L\) provided that the density of the set \(\{k\in\mathbb N: | x_ K-L| \geq \varepsilon \}\) is 0 for each \(\varepsilon >0\) (the density of the set \(M\subset N\) is the number \(\lim_{n\to \infty}M(n)/n\), where \(M(n)\) denotes the number of elements of \(M\) not ...
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A sequence \(\{x_ k\}^{\infty}_{k=1}\) is said to be statistically convergent to \(L\) provided that the density of the set \(\{k\in\mathbb N: | x_ K-L| \geq \varepsilon \}\) is 0 for each \(\varepsilon >0\) (the density of the set \(M\subset N\) is the number \(\lim_{n\to \infty}M(n)/n\), where \(M(n)\) denotes the number of elements of \(M\) not ...
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LEBESGUE DENSITY AND STATISTICAL CONVERGENCE
Real Analysis Exchange, 2021The notion of density points of a Lebesgue measurable subset of real line is well known, as well as the famous Lebesgue Density Theorem. Many authors considered several generalizations of the concept in different directions (see works of \textit{B.~Aniszczyk} and \textit{R.~Frankiewicz} [Bull. Pol. Acad. Sci., Math. 34, 211--213 (1986; Zbl 0591.54002)]
Bienias, Marek, Głąb, Szymon
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Restricting statistical convergence
Acta Mathematica Hungarica, 2011The ``ordinary'' concept of lower- and upper-asymptotic density for a (double) sequence is well known, along with the concept of a sequence being statistically convergent. The authors of the paper under review use an extension of the concept in the following direction: Definition 1. Let \(A\subset\mathbb N\) and denote for every pair \(m,n\in\mathbb N\)
Bhunia, S. +2 more
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Generalized Limits and Statistical Convergence
Mediterranean Journal of Mathematics, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yurdakadim, T. +3 more
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Numerical Functional Analysis and Optimization, 2008
In this work, using the concept of natural density, we introduce the notion of rough statistical convergence. We define the set of rough statistical limit points of a sequence and obtain two statistical convergence criteria associated with this set. Later, we prove that this set is closed and convex. Finally, we examine the relations between the set of
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In this work, using the concept of natural density, we introduce the notion of rough statistical convergence. We define the set of rough statistical limit points of a sequence and obtain two statistical convergence criteria associated with this set. Later, we prove that this set is closed and convex. Finally, we examine the relations between the set of
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WEIGHTED STATISTICAL CONVERGENCE
2009In this paper, the notion of N, pn - summability to generalize the concept of statisticalconvergence is used. We call this new method weighted statistically convergence. We also establish itsrelationship with statistical convergence, C,1-summability and strong n N, p -summability.
Karakaya, Vatan, Chishti, T.A
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2001
In this paper, we define a general sequence space ?m (X) = {x = (xk) : (?m xk) ? X}, (m ? N), where X is any sequence space. We establish some inclusion relations, topological results and we characterize the continuous duals of ?m (X). Furthermore we introduce of ?m-statistical convergence and given inclusion relation between ?m (wp)-convergence and ?m-
Mikail E.T., Nuray F.
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In this paper, we define a general sequence space ?m (X) = {x = (xk) : (?m xk) ? X}, (m ? N), where X is any sequence space. We establish some inclusion relations, topological results and we characterize the continuous duals of ?m (X). Furthermore we introduce of ?m-statistical convergence and given inclusion relation between ?m (wp)-convergence and ?m-
Mikail E.T., Nuray F.
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μ-Statistically Convergent Function Sequences
Czechoslovak Mathematical Journal, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Duman, O., Orhan, C.
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Statistical convergence and measure convergence generated by a single statistical measure
Acta Mathematica Sinica, English Series, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cheng, Li Xin +2 more
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q -Fibonacci statistical convergence
Georgian Mathematical JournalAbstract In this paper, we use the q -Fibonacci band matrix F
Koray İbrahim Atabey +2 more
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