No abstract

In this paper we continue our investigation of the recent summability notion introduced in [Math. Slovaca 69 (4) (2019) 871-890] (where rough weighted statistical convergence for double sequences is discussed over norm linear spaces) and introduce the notion of rough weighted I2-convergence over ?-metric spaces. Also we exercise the behavior of weighted I2-cluster points set over ?-metric spaces. Based on the new notion we vividly discuss some important results and perceive how the existing results are vacillating.

In this paper, we introduce the notion of prime hyperideals and maximal hyperideals in ternary hypersemirings and we study some of their properties. We construct a ternary semiring [Formula: see text], corresponding to a strongly distributive ternary hypersemiring [Formula: see text] and obtain various results among them. We also establish an inclusion preserving bijection between the set of all prime hyperideals of [Formula: see text] and collection of all prime total k-ideals of [Formula: see text].

In this article we elaborately study certain characteristics of the set of all -convergent sequences over various topological spaces. Earlier results of different authors were concerned regarding the closeness property of the sets: set of all bounded statistically convergent sequences, set of all bounded statistically convergent sequences of order ?, set of all bounded I-convergent sequences over the space ?? (??- endowed with the sup-norm) only. On this context apart from this observation other properties (like connected and dense) of all three above mentioned sets have not yet been discussed over any other spaces. Our approach is to examine different behaviors of the set of all I-convergent sequences over different spaces. Finally we are able to exhibit a condition over sequence spaces for which the set of all I-convergent sequences form a closed set.

In this article we recall a remarkable result stated as "For a fixed ?, 0 < ? ? 1, the set of all bounded statistically convergent sequences of order ? is a closed linear subspace of m (m is the set of all bounded real sequences endowed with the sup norm)" by Bhunia et al. (Acta Math. Hungar. 130 (1-2) (2012), 153-161) and to develop the objective of this perception we demonstrate that the set of all bounded statistically convergent sequences of order ? may not form a closed subspace in other sequence spaces. Also we determine two different sequence spaces in which the set of all statistically convergent sequences of order ? (irrespective of boundedness) forms a closed set.