p-frame relative to b-linear functional in n-Banach space

TL;DR

This paper introduces the concept of p-frames relative to b-linear functionals in n-Banach spaces, exploring their properties, stability, and perturbation behavior, thus extending frame theory in this mathematical context.

Contribution

It presents a new definition of p-frames in n-Banach spaces using b-linear functionals and investigates their properties and stability, which has not been previously addressed.

Findings

Cartesian product of two p-frames is again a p-frame

Established perturbation results for p-frames

Proved stability of p-frames under certain conditions

Abstract

Concept of p-frame with the help of b-linear functional in the case of n-Banach space is being presented and its few properties, one of them, Cartesian product of two p-frames again becomes a p-frame, have been discussed. Finally, the perturbation results and the stability of p-frame in n-Banach space with respect to b-linear functional are being studied.