Abstract
We introduce the notions of lacunary -convergence and lacunary -Cauchy in the topology induced by random -normed spaces and prove some important results.
Highlights
Menger [1] generalized the metric axioms by associating a distribution function with each pair of points of a set
We recall some of the basic concepts which will be used in this paper
The vector L is called the IF-limit of the sequence x =, and we write IF-lim x1, x2, . . . , xn−1, x = L
Summary
Menger [1] generalized the metric axioms by associating a distribution function with each pair of points of a set. The idea of Menger was to use distribution function instead of nonnegative real numbers as values of the metric, which was further developed by several other authors In this theory, the notion of distance has a probabilistic nature. The distance between two points x and y is represented by a distribution function Fxy, and for t > 0, the value Fxy(t) is interpreted as the probability that the distance from x to y is less than t Using this concept, Serstnev [4] introduced the concept of probabilistic normed spaces. The notion of lacunary ideal convergence has not been studied previously in the setting of n-normed linear spaces Motivated by this fact, in this paper, as a variant of Iconvergence, the notion of lacunary ideal convergence is introduced in a random n-normed space, and some important results are established. We recall some of the basic concepts which will be used in this paper
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