in this paper‎, ‎following a very recent‎ ‎and new approach‎, ‎we further generalize recently introduced‎ ‎summability methods‎, ‎namely‎, ‎$i$-statistical convergence and‎ ‎$i$-lacunary statistical convergence (which extend the important‎ ‎summability methods‎, ‎statistical convergence and lacunary‎ ‎statistical convergence using ideals of $mathbb{n}$) and‎ ‎introduce the notions of $i$-statis...

In this paper‎, ‎following a very recent‎ ‎and new approach‎, ‎we further generalize recently introduced‎ ‎summability methods‎, ‎namely‎, ‎$I$-statistical convergence and‎ ‎$I$-lacunary statistical convergence (which extend the important‎ ‎summability methods‎, ‎statistical convergence and lacunary‎ ‎statistical convergence using ideals of $mathbb{N}$) and‎ ‎introduce the notions of $I$-statis...

The purpose of this paper is to introduce the concepts of almost lacunary statistical convergence and strongly almost lacunary convergence of sequences of fuzzy numbers. We give some relations related to these concepts. We establish some connections between strongly almost lacunary convergence and almost lacunary statistical convergence of sequences of fuzzy numbers. It is also shown that if a ...

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....

In this paper, the idea of lacunary [Formula: see text]-statistical convergent sequence spaces is discussed which is defined by a Musielak-Orlicz function. We study relations between lacunary [Formula: see text]-statistical convergence with lacunary [Formula: see text]-summable sequences. Moreover, we study the [Formula: see text]-lacunary statistical convergence in probabilistic normed space a...

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.

The definition of lacunary strong convergence is extended to a definition of lacunary strong convergence with respect to a sequence of modulus functions in a Banach space. We study some connections between lacunary statistical convergence and lacunary strong convergence with respect to a sequence of modulus functions in a Banach space.

A lacunary sequence is an increasing integer sequence θ = (kr) such that k0 =0, kr−kr−1 →∞ as r →∞. A sequence x is called Sθ(∆)− convergent to L provided that for each ε > 0, limr(kr − kr−1) {the number of kr−1 < k ≤ kr : |∆xk−L| ≥ ε} = 0, where ∆xk = ∆xk− ∆xk+1. The purpose of this paper is to introduce the concept of ∆ − lacunary statistical convergence and ∆-lacunary strongly convergence an...