Abstract
In this paper, we introduce the λI2 -statistically convergence sequence concepts which are namely λI2 -statistically convergence almost surely (Sλ(I2) a.s.), λI2 -statistically convergence in measure, λI2 -statistically convergence in mean, λI2 -statistically convergence in distribution and λI2 -statistically convergence uniformly almost surely (Sλ(I2) u.a.s.). Additionally, decomposition theorems and relationships among them are presented, further, when reciprocal of one theorem is not satisfied, an counterexample is shown to support the result.
Highlights
Freedman and Sember introduced the concept of a lower asymptotic density and defined the concept of convergence in density, in [1]
We can give the definition of statistical convergence which has been formally introduced by Fast [2] and Steinhaus [3]
The concept of I-convergence of real sequences is a generalization of statistical convergence which is based on the structure of the ideal I of subsets of the set of natural numbers
Summary
Freedman and Sember introduced the concept of a lower asymptotic density and defined the concept of convergence in density, in [1]. The concept of I-convergence of real sequences is a generalization of statistical convergence which is based on the structure of the ideal I of subsets of the set of natural numbers. Das et al [31] in 2020 introduced and studied the notion of statistical convergence of complex uncertain doubl sequence. Kisi and Guler [32] defined λ-statistically convergence of a sequence of uncertain complex variables. Inspired Kisi [33] introduced and studied the convergence concepts of λI -statistically convergence of a sequence of uncertain complex variables by using ideal. Motivate by mentioned above, we make a generalization of λI -convergence of complex uncertain variables on double sequences by using ideal spaces and discuss some relations among them
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