The Generalized difference of $d left(chi^{2 extit{I}}
ight)$ of fuzzy real numbers over $p$ metric spaces defined by Musielak Orlicz function

The Generalized difference of $d left(chi^{2 extit{I}} ight)$ of fuzzy real numbers over $p$ metric spaces defined by Musielak Orlicz function

**Authors : **

Vandana ^{a} , Deepmala ^{b,∗} and N. Subramanian^{ c}

**Author Address : **

^{a }Department of Management Studies, Indian Institute of Technology Madras, Tamil Nadu-600 036, India

^{b }Mathematics Discipline, PDPM Indian Institute of Technology, Design & Manufacturing (IIITDM) Jabalpur-482005, (M.P.) India.

^{c }Department of Mathematics, SASTRA University, Thanjavur-613401, India.

*Corresponding author.

**Abstract : **

In this article we introduce the sequence spaces $left[chi^{2q}_{fmu },left|left(dleft(x_{1} ight),dleft(x_{2} ight),cdots, dleft(x_{n-1} ight) ight) ight|_{p} ight]^{ extit{I}left(F ight)}$ and $left[Lambda^{2q}_{fmu },left|left(dleft(x_{1} ight),dleft(x_{2} ight),cdots, dleft(x_{n-1} ight) ight) ight|_{p} ight]^{ extit{I}left(F ight)},$ associated with the differential operator of sequence space defined by Musielak. We study some basic topological and algebraic properties of these spaces. We also investigate some inclusion relations related to these spaces.

**Keywords : **

Analytic sequence, double sequences, $chi^{2}$ space, difference sequence space,Musielak - Orlicz function, $p-$ metric space, Ideal; ideal convergent; fuzzy number; multiplier,differential operato

**DOI : **

**Article Info : **

*Received : * November 12, 2016; *Accepted : * April 15, 2017.