Rough convergence of double sequences of fuzzy numbers

In this paper, we define the concepts of rough convergence and rough Cauchy sequence of double sequences of fuzzy numbers. Then, we investigate some relations between rough limit set and extreme limit points of such sequences.     

On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space

The concept of statistical convergence was introduced by Fast [H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951) 241–244] which was later on studied by many authors. In [J.A. Fridy, C. Orhan, Lacunary statistical convergence, Pacific J. Math. 160 (1993) 43–51], Fridy and Orhan introduced the idea of lacunary statistical convergence. Quite recently, the concept of statistical convergence of double sequences has been studied in intuitionistic fuzzy normed space by Mursaleen and Mohiuddine [M. Mursaleen, S.A. Mohiuddine, Statistical convergence of double sequences in intuitionistic fuzzy normed spaces, Chaos Solitons Fractals (2008), doi:10.1016/j.chaos.2008.09.018]. In this paper, we study lacunary statistical convergence in intuitionistic fuzzy normed space. We also introduce here a new concept, that is, statistical completeness and show that IFNS is statistically complete but not complete.     

On statistical and p -Cesaro convergence of fuzzy numbers

In this paper, the concept of stronglyp-Cesaro summability of sequences of fuzzy numbers is introduced. The relationship between statistical convergence and stronglyp-Cesaro summability is discussed.     

Almost sure convergence for the maxima of strongly dependent stationary Gaussian vector sequences

In this paper, we prove the almost sure limit theorem of the maxima for a kind of strongly dependent stationary Gaussian vector sequences.     

Almost everywhere convergence of lacunary partial sums of Vilenkin-Fourier series

We prove that if , and is any lacunary sequence of positive integers, then the sequence of th partial sums of Vilenkin-Fourier series of converges almost everywhere to .

     

On the Cesàro convergence of sequences of fuzzy numbers

In this paper we have determined necessary and sufficient Tauberian conditions under which convergence follows from (C,1)-convergence of sequences of fuzzy numbers.     

Almost overcomplete and almost overtotal sequences in Banach spaces

We introduce the new concepts of almost overcomplete sequence in a Banach space and almost overtotal sequence in a dual space. We prove that any of such sequences is relatively norm-compact and we present several applications of this fact.     

On fuzzy almost continuous convergence in fuzzy function spaces

In this paper, we study the fuzzy almost continuous convergence of fuzzy nets on the set FAC(X, Y) of all fuzzy almost continuous functions of a fuzzy topological space X into another Y. Also, we introduce the notions of fuzzy splitting and fuzzy jointly continuous topologies on the set FAC(X, Y) and study some of its basic properties.     

Generalized statistical convergence and statistical core of double sequences

In this paper we extend the notion of A-statistical convergence to the （λ,μ）statistical convergence for double sequences x =（xjk）. We also determine some matrix transformations and establish some core theorems related to our new space of double sequences Sλ,μ.     

On the difference spaces of almost convergent and strongly almost convergent double sequences

In this paper, we study the difference spaces \({\mathcal {F}}(\varDelta )\), \({\mathcal {F}}_0(\varDelta )\), \({\mathcal {[F]}}(\varDelta )\) and \({\mathcal {[F]}}_0(\varDelta )\) of double sequences obtained as the domain of four-dimensional backward difference matrix \(\varDelta \) in the spaces \({\mathcal {F}}\), \({\mathcal {F}}_{0}\), \({\mathcal {[F]}}\) and \({\mathcal {[F]}}_{0}\) of almost convergent, almost null, strongly almost convergent and strongly almost null double sequences; respectively. We examine general topological properties of those spaces and give some inclusion theorems. Furthermore, we deal with their dual spaces.

     

On the strong almost convergence of double sequences

In this paper, necessary and sufficient conditions that the real doubly infinite matrixA sums every strongly almost convergent double sequence, leaving the limit invariant, have been determined.     

Strong convergence theorems for strongly nonexpansive sequences

The aim of this paper is to prove a strong convergence theorem for a pair of sequences of nonexpansive mappings in a Hilbert space, where one of them is a strongly nonexpansive sequence, and provide some applications of the theorem.     

Almost convergence and a core theorem for double sequences

The idea of almost convergence was introduced by Moricz and Rhoades [Math. Proc. Cambridge Philos. Soc. 104 (1988) 283-294] and they also characterized the four dimensional strong regular matrices. In this paper we define the M-core for double sequences and determine those four dimensional matrices which transform every bounded double sequence x=[x_jk] into one whose core is a subset of the M-core of x.     

Weak statistical convergence and weak filter convergence for unbounded sequences

For every weakly statistically convergent sequence (xn) with increasing norms in a Hilbert space we prove that . This estimate is sharp. We study analogous problem for some other types of weak filter convergence, in particular for the Erdös-Ulam filters, analytical P-filters and Fσ filters. We present also a refinement of the recent Aron-Garcia-Maestre result on weakly dense sequences that tend to infinity in norm.