Some further studies on strong ℐλ-statistical convergence in probabilistic metric spaces

We prove some basic properties of strong ℐ λ {\mathcal{I}_{\lambda}} -statistical convergence of sequences in probabilistic metric spaces and introduce the notion of strong ℐ λ {\mathcal{I}_{\lambda}} -statistical cluster point. We also introduce the notion of strong ℐ λ {\mathcal{I}_{\lambda}} -statistical Cauchy sequences in probabilistic metric spaces. Further, we establish a connection between strong ℐ λ {\mathcal{I}_{\lambda}} -statistical convergence and strong ℐ λ {\mathcal{I}_{\lambda}} -statistical Cauchy sequences.

Limits, Sequences, and Sums

This chapter first introduces the concepts of real sequences, Cauchy sequences, limits, and cluster points. The chapter then discusses functions of a real variable, continuity concepts, convergence concepts for sequences of functions, summability and order of magnitude relations, inequalities for sums, regular variation, and limit concepts for arrays.

ON I- CONVERGENCE OF SEQUENCES IN GRADUAL NORMED LINEAR SPACES

In this paper, we introduce the concepts of $\mathcal{I}$ and $\mathcal{I^{*}}-$convergence of sequences in gradual normed linear spaces. We study some basic properties and implication relations of the newly defined convergence concepts. Also, we introduce the notions of $\mathcal{I}$ and $\mathcal{I^{*}}-$Cauchy sequences in the gradual normed linear space and investigate the relations between them.

I_2-LOCALIZED DOUBLE SEQUENCES IN METRIC SPACES

In this article, the notions of $ I_{2} $-localized and $ I_{2}^{*} $-localized sequences in metric spaces are defined. Besides, we study some properties associated to $ I_{2} $-localized and $ I_{2} $-Cauchy sequences. On the other hand, we define the notion of uniformly $ I_{2} $-localized sequences in metric spaces.

Lacunary Statistical Delta 2 2-Quasi Cauchy Double Sequences

In this paper, we have introduced the extension of recently introduced notion of summability of lacunary statistical delta 2 quasi Cauchy sequences to double sequences and established some essential results using analogy.

Strongly $\lambda$-Statistically and Strongly Vallée-Poussin Pre-Cauchy Sequences in Probabilistic Metric Spaces

We introduce the notions of strongly $\lambda$-statistically pre-Cauchy and strongly Vall´ee-Poussin pre-Cauchy sequences in probabilistic metric spaces endowed with strong topology. And we show that these two new notions are equivalent. Strongly $\lambda$-statistically convergent sequences are strongly $\lambda$-statistically pre-Cauchy sequences, and we give an example to show that there is a sequence in a probabilistic metric space which is strongly $\lambda$-statistically pre-Cauchy but not strongly $\lambda$-statistically convergent.

SEQUENCE OF SOFT POINTS IN SOFT Δ-METRIC SPACES

In this paper, we have constructed a sequence of soft points in one soft set with respect to a fixed soft point of another soft set. The convergence and boundedness of these sequences in soft Δ-metric spaces are defined and their properties are established. Further, the complete soft Δ-metric spaces are introduced by defining soft Δ-Cauchy sequences.