Aktuğlu and Gezer [1] introduced the concepts of lacunary equistatistical convergence, lacunary statistical pointwise convergence and lacunary statistical uniform convergence for sequences of functions. Recently, Kaya and Gönül [11] proved some analogs of the Korovkin approximation theorem via lacunary equistatistical convergence by using test functions 1, x 1+x , y 1+y , ( x 1+x )2+( y 1+y )2....

The definition of lacunary strong convergence with respect to a modulus is extended to a definition of lacunary strong A-convergence with respect to a modulus when A = (aik) is an infinite matrix of complex numbers. We study some connections between lacunary strong A-convergence with respect to a modulus and lacunary A-statistical convergence.

This paper presents the following definition which is a natural combination of the definition for asymptotically equivalent of order α, where 0 < α 6 1, I-statistically limit, and I-lacunary statistical convergence for sequences of sets. Let (X, ρ) be a metric space and θ be a lacunary sequence. For any non-empty closed subsets Ak, Bk ⊆ X such that d(x,Ak) > 0 and d(x,Bk) > 0 for each x ∈ X, we...

For a finite measure λ, let L0(λ) denote the space of λ-measurable functions equipped with the topology of convergence in measure. We prove that a series in L0(λ) is subseries (or unconditionally) convergent provided each of its lacunary subseries converges. A series in a topological vector space is said to be subseries convergent if each of its subseries converges. As is well known, a subserie...

The purpose of this article is to investigate lacunary ideal convergence sequences in neutrosophic normed space (NNS). Also, an original notion, named sequence NNS, defined. $% \mathcal{I}$-limit points and $\mathcal{I}$-cluster NNS have been examined. Furthermore, Cauchy $\mathcal{I}$-Cauchy are introduced some properties these notions studied.

In the present paper we introduce and study some lacunary difference bicomplex sequence spaces by means of Orlicz functions. We make an effort to algebraic topological properties these spaces. also show that are complete paranormed Further, inclusion relations between interesting examples established. Finally, prove results on modified complex Banach Algebra in third section paper.

In this report, we first review some algebraic and topological structures relevant to some difference sequence spaces which were constructed in comparison with the classical spaces 0 c , c and ∞ l .Then we review Cesàro and lacunary summability methods for difference sequences. Lastly, we review algebraic duals for several different kinds of difference sequence spaces.

The main object of this paper is to introduce and study a new concept of f-Wijsman lacunary statistical convergence of sequences of sets, where f is an unbounded modulus. The definition of Wijsman lacunary strong convergence of sequences of sets is extended to a definition of Wijsman lacunary strong convergence with respect to a modulus for sequences of sets and it is shown that, under certain ...