CrossRef 2013 5 sitasi

On the class gamma and related classes of functions

Edward Omey

Abstrak

The gamma class ??(g) consists of positive and measurable functions that satisfy f(x + yg(x))/f(x) ? exp(?y). In most cases the auxiliary function g is Beurling varying and self-neglecting, i.e., g(x)/x ? 0 and g??0(g). Taking h = log f, we find that h?E??(g, 1), where E??(g, a) is the class of positive and measurable functions that satisfy (f(x + yg(x))? f(x))/a(x) ? ?y. In this paper we discuss local uniform convergence for functions in the classes ??(g) and E??(g, a). From this, we obtain several representation theorems. We also prove some higher order relations for functions in the class ??(g) and related classes. Two applications are given.

Penulis (1)

Edward Omey

Format Sitasi

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Omey, E. (2013). On the class gamma and related classes of functions. https://doi.org/10.2298/pim1307001o

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Informasi Jurnal

Tahun Terbit: 2013
Bahasa: en
Total Sitasi: 5×
Sumber Database: CrossRef
DOI: 10.2298/pim1307001o
Akses: Terbatas