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International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2008 The goal of this work is the further development of neoclassical analysis, which extends the scope and results of the classical mathematical analysis by applying fuzzy logic to conventional mathematical objects, such as functions, sequences, and series.
Mark Burgin, Oktay Duman
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Strongly Statistical Convergence
Ukrainian Mathematical Journal, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kaya, U., Aral, N. D.
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Generalized statistical convergence
Information Sciences, 2004A new concept of statistical convergence, \(\mathcal{B}\)-statistical convergence, that includes the usual statistical convergence, \(A\)-statistical convergence, lacunary statistical convergence, as particular cases, is introduced. Correspondingly, \(\mathcal{B}\)-statistical limit points, \(\mathcal{B}\)-statistical cluster points, etc., are defined ...
Mohammad Mursaleen, Osama H. H. Edely
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On Almost Convergent and Statistically Convergent Subsequences
Acta Mathematica Hungarica, 2001A bounded sequence \(s=(s_{n})\) is almost convergent to \(L\) if \[ \lim_{k}\frac{1}{k}\sum_{i=0}^{n-1}s_{n+i}=L,\quad \text{uniformly in }n . \] We write \(f\)-\(\lim s=L\) and \(\mathbf F=\{s=(s_{n}): f\text{-}\lim s=L\text{ for some }L\}.\) The sequence \(s=(s_{n})\) is called statistically convergent to \(L\) provided that \(\lim_{n}n^{-1}\left ...
Miller, H. I., Orhan, C.
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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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On the Convergence of Statistical Search
IEEE Transactions on Systems, Man, and Cybernetics, 1976The convergence of statistical (random) search for the minimization of an arbitrary multimodal functional Q(w) is dealt with by using the theorems of convergence of random processes of Braverman and Rozonoer. It is shown that random search can be regarded as a gradient algorithm in the Q-domain.
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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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On lacunary ?-statistical convergence
Information Sciences, 2004The purpose of this paper is to introduce two new spaces and also to define stσ and stθσ of strongly σ-statistically convergent and lacunary strongly σ-statistically convergent sequences, respectively. Also, we give some inclusion relations involving these spaces.
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Weighted Lacunary Statistical Convergence
Iranian Journal of Science and Technology, Transactions A: Science, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sakarya Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü +2 more
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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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