Some new spaces of lacunary f-statistical A-convergent sequences of order α

Abstract

We study the concept of density for sets of natural numbers in some lacunary Aconvergent sequence spaces. Also we are trying to investigate some relation between the ordinary convergence and module statistical convergence for evey unbounded modulus function. Morever we also study some results on the newly defined lacunary f -statistically A-convergent sequence spaces with respect to some Musielak-Orlicz function.

On lambda-statistical convergence using f-density

“…In recent years, the concept of statistical convergence of sequences which was first introduced by Fast [8] as an extension of the usual concept of sequential limits, has also been used as a tool by many mathematicians to solve many open problems in the area of sequence spaces and summability theory and some other applications as well. One may refer to ( [6], [16], [12], [14], [17], [19], [21], [22], [23], [25], [31], [10]).…”

On new f-statistical convergence in probabilistic normed spaces

“…They studied and characterized the generalization of this notion of f -density with statistical convergence and proved that ordinary convergence is equivalent to the module statistical convergence for every unbounded modulus function. Savaş and Borgohain [17] introduced some new spaces of lacunary f -statistical A-convergent sequences of order α.…”