A New Definition of Limit of Periodic Function and Periodic g-Contractive Mapping at Infinity | Chapter 08 | Advances in Mathematics and Computer Science Vol. 1
Limit is a
basic concept of calculus. However, according to the updated definition, the
limit of periodic function at infinity is not in existence. This conclusion of
description does not suit with the periodic phenomenon. For example, the
temperature on earth is changed periodically every year since the birth of the
earth (viewed as t=0). Today (viewed as t →∞) the temperature on earth is
continuing. Continuation means that the limit exists. In this paper, a new
definition of limit of periodic function and periodic g-contractive mapping at
infinity is defined by the value of its initial point based on transformation
of variables. Similar definition is made for g- contractive ratio of periodic
g-contractive mapping with k-related fixed points. These definitions can be
used to describe the k-polar problems and calculation the limit of combinations
of periodic functions at infinity. Furthermore, the new definition on
contractive ratio of periodic iterative g-contractive mapping at infinity can
help us to find the constant G and improves the application of the periodic
iterative g-contractive mapping theorem.
Author Details:
Tian-Quan Yun
School
of Civil Engineering and Transportation, South China University of Technology,
Guangzhou, 510641, P.R. China.
Comments
Post a Comment