Some Basic Results on the Sets of Sequences with Geometric Calculus

被引：14

作者：

Turkmen, Cengiz ^{[1
]}

Basar, Feyzi ^{[2
]}

机构：

[1] Fatih Univ, Grad Sch Sci & Engn, Hadimkoy Campus, TR-34500 Istanbul, Turkey

[2] Fatih Univ, Fac Arts & Sci, Dept Math, TR-34500 Istanbul, Turkey

来源：

FIRST INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2012) | 2012年 / 1470卷

关键词：

Geometric calculus; Algebraic structures with respect to geometric calculus; Geometric sequence spaces;

D O I：

10.1063/1.4747648

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

As an alternative to the classical calculus, Grossman and Katz [Non-Newtonian Calculus, Lee Press, Pigeon Cove, Massachusetts, 1972] introduced the non-Newtonian calculus consisting of the branches of geometric, anageometric and bigeometric calculus. Following Grossman and Katz, we construct the field C(G) of geometric complex numbers and the concept of geometric metric. Also we give the triangle and Minkowski's inequalities in the sense of geometric calculus. Later we respectively define the sets w(G), l(infinity)(G), c(G), c(0)(G) and l(p)(G) of all, bounded, convergent, null and p-absolutely summable sequences, in the sense of geometric calculus and show that each of the set forms a complete vector space on the field C(G).

引用

页码：95 / 98

页数：4