Generalized Geometric Difference Sequence Spaces and its duals

TL;DR

This paper introduces generalized geometric difference sequence spaces, proves they are Banach spaces, explores their inclusion properties, and computes their dual spaces, expanding the theoretical framework of sequence space analysis.

Contribution

It defines new generalized geometric difference sequence spaces and establishes their Banach space structure, inclusion relations, and dual spaces, which are novel contributions.

Findings

The spaces are Banach spaces.

Inclusion properties are established.

Dual spaces are explicitly computed.

Abstract

Objective of this paper is to introduce the generalized geometric difference sequence spaces $l_\infty^{G}(\Delta^m_G), c^G(\Delta^m_G), c_0^{G}(\Delta^m_G)$ and to prove that these are Banach spaces. Then we prove some inclusion properties. Also we compute their dual spaces.