In this article, we have constructed generalized q-difference Motzkin sequence spaces [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] by composing q-Motzkin matrix with generalized q-difference matrix in the spaces [Formula: see text], respectively and explore their topological properties. We determine the bases for [Formula: see text] and [Formula: see text] and compute α-, β- and γ-duals of the newly defined spaces. Further, we characterize some class of matrix mappings from the spaces [Formula: see text] and [Formula: see text] to the spaces [Formula: see text]. Lastly, compact operators are characterized on the spaces [Formula: see text] using Hausdorff measure of noncompactness.

In this article, we present and investigate new type of sequence spaces called by almost convergent Motzkin sequence spaces. We demonstrate that the newly introduced spaces are linearly isomorphic to the spaces of all almost convergent sequences and compute the beta-dual. Additionally, we characterize (9i, Z) and (Z, 9i) for any given sequence space Z, and also determine the necessary and sufficient condition on a matrix P such that for every bounded sequence u, BM-core(Pu) subset of K-core(u) and B-M-core(Pu) subset of st-core(u).

In this article, we introduce the notions of deferred Euler statistical convergence with respect to power series as well as g-deferred Euler statistical convergence in the sense of power series method for double sequences of real numbers. Furthermore, we establish applications of these convergences in the form of a Korovkin-type approximation theorem. Finally, we determine the rate of convergence.

In this paper, the concepts of Riesz lacunary statistical convergence, Riesz lacunary strong convergence, and Riesz lacunary uniform integrability of real sequences within the framework of power series are introduced and studied. Fundamental relationships among these notions are established, particularly in terms of uniform integrability. A characterization of Riesz lacunary uniform integrability is provided. Furthermore, these definitions by incorporating a modulus function are explored, and significant interrelations among these concepts are investigated.

The paper aims to investigate lambda-statistical convergence using modulus function and a generalized difference operator for double sequences of functions for order gamma is an element of (0, 1]. Further, we prove that the statistical convergence in the newly formed sequence spaces is not well defined for gamma > 1. Finally, we examine relevant inclusion relations concerning lambda-statistical convergence and strongly lambda-summable in the environment of the newly defined classes of double sequences of functions. Some interesting examples related to the examined results are also discussed in this paper.

In this paper, we introduce and study a new type of convergences using statistical convergence via the power series method and measurable convergence. We also study their relationship with other convergences. Further, we demonstrate Korovkin-type approximation theorems for double sequences of positive linear operators using these newly specified convergences, and we also provide illustrations that demonstrate how our proven theorems are better than their classical counterparts. Finally, we have determined rates of statistical product measurable convergence using the power series approach and the modulus of continuity.

The central objective of this paper is to investigate the lacunary statistical convergence of order [Formula: see text] and strong lacunary summability of order [Formula: see text] for sequences of fuzzy functions by using the modulus function and a regular matrix. We examine the relevant inclusion relations between these spaces under specific conditions. Additionally, we study properties related to these spaces and establish several interesting results.

In this paper, we define and study strongly deferred Ces & agrave;ro summable, strongly Ces & agrave;ro summable, m-statistical convergence and m-deferred statistical convergence of real-valued Lebesgue measurable functions of two variables. Further, we present illustrative examples in support of our definitions. Also, we examine some properties and relations among these concepts under some restrictions. In addition, we present illustrative examples to show the essentiality of these restrictions.

In this paper, we introduce the notions of product measurable convergence, deferred Cesàro statistical product measurable convergence and deferred Cesàro statistical Lebesgue product measurable convergence for sequences of measurable functions on product measure spaces. We establish some fundamental relations among these convergences and also give several explanatory examples in support of our definitions and results. Finally, as an application, we prove a new version of Korovkin-type approximation theorems for sequences of measurable functions on product measure spaces by using the notion of deferred Cesàro statistical Lebesgue product measurable convergence.