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

  • 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.
Keywords: D-metric spaces, Logarithmic hyperbolic classes, Composition operators


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.


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How to Cite
A. Kamal and T. Yassen, “D-metric Spaces and Composition Operators Between Hyperbolic Weighted Family of Function Spaces”, CUBO, A Mathematical Journal, vol. 22, no. 2, pp. 215–231, Aug. 2020.