Second Order Quantum Difference Operator of Lacunary Weak Convergence of Sequences

Abstract

In this article, we introduce the concept of the second-order quantum difference operator and examine its role within the framework of lacunary weak convergence of sequences. This operator provides a new perspective in the study of sequence spaces, offering fresh insights into their structural and func tional properties. We investigate several key algebraic and topological features of these spaces, including properties like symmetry, strict convexity, and uniform convexity, which are crucial for understanding their behavior and applications. Additionally, we establish and discuss several important inclusion relations between the sequence spaces defined by this operator, which helps in characterizing their connections and hierarchy. The exploration of these inclusion relations not only broadens the theoretical scope of sequence spaces but also paves the way for future research in functional analysis and quantum calculus. This study provides a comprehensive framework for further investigation into advanced topics in sequence space theory