On the Inner-Product Spaces of Complex Interval Sequences

Authors : Halise LEVENT, Yılmaz YILMAZ, Hacer BOZKURT

Pages : 180-188

Doi:10.33434/cams.1200557

View : 17 | Download : 9

Publication Date : 2022-12-30

Article Type : Research Paper

Abstract :In recent years, there has been increasing interest in interval analysis. Thanks to interval numbers, many real world problems have been modeled and analyzed. Especially, complex intervals have an important place for interval-valued data and interval-based signal processing. In this paper, firstly we introduce the notion of a complex interval sequence and we present the complex interval sequence spaces $\\mathbb{I}insert ignore into journalissuearticles values(w);$ and $\\mathbb{I}insert ignore into journalissuearticles values(l_{p});$, $1\\leq p<\\infty$. Secondly, we show that these sequence spaces have an algebraic structure called quasilinear space. Further, we construct an inner-product on $\\mathbb{I}insert ignore into journalissuearticles values(l_{2});$ and we show that $\\mathbb{I}insert ignore into journalissuearticles values(l_{2});$ is an inner-product quasilinear space.
Keywords : Complex interval, Complex interval sequence, Inner product quasilinear space, Consolidate space