Related papers: Some new $I_\lambda$-lacunary statistical converge…
In this article we introduce and study the lacunary arithmetic convergent sequence space $AC_{\theta}$. Using the idea of strong Ces\`{a}ro summable sequence and arithmetic convergence we define $AC_{\sigma_1}$ and study the relations…
This paper is discussing about the notion of some new types of convergences namely $I$-convergence and $I^*$-convergence of a $\Delta$-measurable function $f$ on time scales $T$ by considering ideal on time scales $T$. This idea is further…
This paper introduces statistical order convergence and its pointwise variant for sequences of order bounded operators between Riesz spaces. We establish fundamental properties: uniqueness of the limit, stability under lattice operations,…
The aim of this paper is investigating of Orlicz spaces with exponential function and correspondence Orlicz norm: we introduce some new equivalent norms, obtain the tail characterization, study the product of functions in Orlicz spaces etc.…
In this article, we study certain transcendental function spaces arising in potential theory within the framework of Orlicz spaces. Specifically, we generalize Bessel and Lizorkin-Triebel spaces to the nonstandard setting of Orlicz spaces.…
This paper aims to extend the concept of stochastic $\Sigma$-convergence to the framework of Orlicz-Sobolev spaces in order to deals with coupled stochastic and deterministic homogenization problems in this type of spaces. Thus, this…
We study intermediate-scale statistics for the fractional parts of the sequence $(\alpha a_n)_{n=1}^{\infty}$, where $(a_n)_{n=1}^{\infty}$ is a positive, real-valued lacunary sequence, and $\alpha\in\mathbb{R}$. In particular, we consider…
In this paper, we have introduced first the notion of rough $I^*$-convergence in a normed linear space as an extension work of rough $I$-convergence and then rough $I^K$-convergence in more general way. Then we have studied some properties…
We establish uniform estimates for order statistics of sequences of independent identically distributed random variables with log-concave distribution in terms of Orlicz norms associated with the distribution function of the random…
In this paper we present the theory of lacunary trigonometric sums and lacunary sums of dilated functions, from the origins of the subject up to recent developments. We describe the connections with mathematical topics such as…
In this article, we show that Orlicz-Lorentz spaces $\ell^n_{M,a}$, $n\in\mathbb N$ with Orlicz function $M$ and weight sequence $a$ are uniformly isomorphic to subspaces of $L_1$ if the norm $\|\cdot\|_{M,a}$ satisfies certain Hardy-type…
In this article we develop the theory of $H$-Orlicz space generated by generalised Young function. Modular convergence of $H$-Orlicz space for the case of vector-valued functions and norm convergence in $\mcH^\theta(X, \bar{\mu})$ where $X$…
In this paper, the concept of Musielak N-functions and Musielak-Orlicz spaces generated by them well be introduced. Facts and results of the measure theory will be applied to consider properties, calculus and basic approximation of Musielak…
In this paper, we deal with the family of Steklov sampling operators in the general setting of Orlicz spaces. The main result of the paper is a modular convergence theorem established following a density approach. To do this, a Luxemburg…
We present a new rigorous approach based on Orlicz spaces for the description of the statistics of large regular statistical systems, both classical and quantum. This approach has the advantage that statistical mechanics is much better…
The purpose of this paper is twofold. First, the definition of new statistical convergence with Fibonacci sequence is given and some fundamental properties of statistical convergence are examined. Second, approximation theory worked as a…
Given a frequency $\lambda$, we study general Dirichlet series $\sum a_n e^{-\lambda_n s}$. First, we give a new condition on $\lambda$ which ensures that a somewhere convergent Dirichlet series defining a bounded holomorphic function in…
In this paper we look for the existence of large linear and algebraic structures of sequences of measurable functions with different modes of convergence. Concretely, the algebraic size of the family of sequences that are convergent in…
In this paper, we extend the Marcinkiewicz--Zygmund inequality to the setting of Orlicz and Lorentz spaces. Furthermore, we generalize a Kadec--Pe{\l}czy\'nski-type result -- originally established by the first and third authors for $L^p$…
We investigate summable analogues of the classical Ivashev-Musatov Theorem and threshold phenomenons alike. In the setting of weighted $\ell^1$ and Orlicz sequence spaces, we exhibit elements with critically pathological support and range,…