A Study of Some Different Concepts of Symmetry on the Real Line

Abstract

Recently, different concepts of symmetry on R ⁺ such as R-symmetry, log-symmetry, and double symmetry are studied. Analogous concepts and their properties of these symmetries on R will be studied in this work. Based on skewing representation and previous studies, characterizations of double symmetry on R will be given. Among others, some interesting examples of the so-called I-symmetry, that is the analogue of log-symmetry on R, will also be presented.

Keywords:

• Characterization
• Double symmetry
• I-symmetry
• Log-symmetry
• R-symmetry
• Skewing representation

Mathematics Subject Classification:

• Primary, 62E10
• Secondary, 60E05

Acknowledgments

The authors are very grateful to the referees for many constructive and useful comments that greatly enhanced the clarity of this article.

Support for this research was provided in part by the National Science Council of the Republic of China, Grant No. NSC 98-2118-M-390-001-MY2.