ON PARANORMED I-CONVERGENT SEQUENCE SPACES OF INTERVAL NUMBERS

VAKEEL. A. KHAN; MOHD  SHAFIQ; KHALID  EBADULLAH

ON PARANORMED I-CONVERGENT SEQUENCE SPACES OF INTERVAL NUMBERS

Authors

VAKEEL. A. KHAN Department of Mathematics, A.M.U, Aligarh-202002, India
MOHD SHAFIQ Department of Mathematics, A.M.U, Aligarh-202002, India
KHALID EBADULLAH Department of Applied Mathematics, Zakir Husain College of Engineering and Technology, AligarhMuslim University , Aligarh-202002, India

Keywords:

Interval numbers, Ideal, Filter, I-convergent sequence, Solid and monotone space, Banach space

Abstract

In this article we introduce and study the paranormed I-convergent sequence spaces $\mathcal{C}^{I}(\mathcal{\bar{A}},p)$, $\mathcal{C} ^{I}_{0}(\mathcal{\bar{A}},p)$, $\mathcal{M}^{I}_{\mathcal{C}}(\mathcal{\bar{A}},p)$ and $\mathcal{M}^{I}_{\mathcal{C_{\circ}}}(\mathcal{\bar{A}},p)$ on the sequence of interval numbers with the help of a bounded sequence $p=(p_k)$ of strictly positive real numbers. We study some topological and algebraic properties and some inclusion relations on these spaces.