Sequences are used in almost every branch of business, science, and engineering. In the classical approach, there are several methods and procedures to find the limit of the sequence. In some situations, we are not able to find out whether the limit of the sequence exists or not. Still, there is an idea of the generalized limit or weak limit of a sequence which may help for the problem under consideration. Summability theory gives a generalized concept of the convergence of sequences and series where even a limit to divergent sequences or series can be assigned under the name of statistical convergence. In this work we discuss the idea of λ -statistical convergence of order α is formed in Probabilistic Normed Spaces and λ -statistical convergence in random n-normed spaces. This concept is more generalized than λ -statistical convergence in these spaces.
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