arXiv subjects
Publications and source records attributed to Stuti Borgohain.
In this article, we study about the $λ$-statistical convergence with respect to the density of moduli and find some results related to statistical convergence as well. Also we introduce the concept of $f_λ$-summable sequence and try to investigate some relation between the $f_λ$-summability and module $% λ$-statistical convergence.
In this paper, we introduce some new $I_λ$-lacunary statistically convergent sequence spaces of order $α$ defined by a Musielak-Orlicz function. We study some relations between $I_λ$-lacunary statistically convergence with lacunary $I_λ$-summable sequences. Moreover we also study about the $I_λ$-lacunary statistically convergence of sequences in topological groups and give some important inclusion theorems.
We study some new strongly almost lacunary statistical $A$-convergent sequence space of order $α$ defined by a Musielak-Orlicz function. We also give some inclusion relations between the newly introduced class of sequences with the spaces of strongly almost lacunary $A$-convergent sequence of order $α$. Moreover we have examined some results on Musielak-Orlicz function with respect to these spaces.
We study the concept of density for sets of natural numbers in some lacunary $A$-convergent 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.
In this research article, we establish some identities and estimates for the operator norms and the Hausdorff measures of noncompactness of certain operators on some lacunary difference sequence spaces defined by Orlicz function. Moreover, we apply our results to characterize some classes of compact operators on those spaces by using the Hausdorff measure of noncompactness.
In this paper we introduced the generalized difference Cesaro sequence spaces of fuzzy real numbers defined by Orlicz function. We study some topological properties of these spaces. We obtain some inclusion relations involving these sequence spaces. These notions generalize many notions on difference Cesaro sequence spaces.