D-metric Spaces and Composition Operators Between Hyperbolic Weighted Family of Function Spaces

A. Kamal; T.I. Yassen

doi:10.4067/S0719-06462020000200215

DOI:

https://doi.org/10.4067/S0719-06462020000200215

Abstract

The aim of this paper is to introduce new hyperbolic classes of functions, which will be called \({\mathcal{B}}^{*} _{\alpha,\;\log}\) and \({ F ^{*}_{\log}}(p,q,s)\) classes. Furthermore, we introduce \(D\)-metrics space in the hyperbolic type classes \({\mathcal{B}}^{*} _{\alpha,\;\log}\) and \( { F ^{*}_{\log}}(p,q,s)\). These classes are shown to be complete metric spaces with respect to the corresponding metrics. Moreover, necessary and sufficient conditions are given for the composition operator \(C_\phi\) to be bounded and compact from \({\mathcal{B}}^{*}_{\alpha,\;\log}\) to \({F ^{*}_{\log}}(p,q,s)\) spaces.

Keywords

D-metric spaces , Logarithmic hyperbolic classes , Composition operators

A. Kamal Port Said University, Faculty of Science, Department of Mathematics and Computer Science, Port Said, Egypt.
T.I. Yassen The Higher Engineering Institute in Al-Minya (EST-Minya) Minya, Egypt.

Pages: 215–231
Date Published: 2020-08-22
Vol. 22 No. 2 (2020)

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