$$A$$ -distributional summability in topological spaces

Lacunary distributional convergence in topological spaces

“…where ∂G is the boundary of G [18]. The aim of the present paper is to study a variant of distributional convergence in which the nonnegative regular summability matrix A = (a nk ) is replaced by C θ matrix and to obtain similar results given in [12] for topological spaces.…”

“…Therefore, many authors have restricted the scope by assuming either the topological space to have a group structure or a linear structure. Recently, some authors have studied some summability methods that directly can be defined in arbitrary Hausdorff spaces such as A-statistical convergence and A-distributional convergence (see e.g., [2,15,[17][18][19]).…”

“…For example, properties of statistically convergent scalar sequences investigated by Fridy [10] and Salát [16]. Furthermore, the concept of statistical convergence has been studied in topological spaces by many authors (see e.g., [2,15,18]). Moreover, a generalization of the statistical convergence which is called ideal convergence can be studied in topological spaces (see e.g., [6,7]).…”

“…al. [18] investigated the relationship between these concepts and they observed that Adistributional convergence is equivalent to A-statistical convergence for a particular degenerate distribution. In [12], the authors established some inclusion relations between the concept of statistical convergence and lacunary statistical convergence.…”

“…al. [18] has proved that A-statistical convergence is the special case of A-distributional convergence. This result with Definition 1.1 entails the following remark immediately: Remark 1.2.…”