Skip to main content

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.

Read full article: http://bp.bookpi.org/index.php/bpi/catalog/view/46/227/387-2
View Volume: https://doi.org/10.9734/bpi/amacs/v1
Labels:

Comments

Post a Comment

Popular posts from this blog

Greening Regional Airports: A Vision for Carbon Neutral Infrastructure | Chapter 12 | Contemporary Perspective on Science, Technology and Research Vol. 3

 This study provides an overview of the energy demand of a regional airport, divided into individual time horizons. The electrification of aircraft systems raises the question of whether airports will be among the largest electricity consumers in our infrastructure in the future. Sustainability and especially emission reductions are significant challenges for airports that are currently being addressed. The Clean Sky 2 project GENESIS addresses the environmental sustainability of hybrid-electric 50-passenger aircraft systems in a life cycle perspective to support the development of a technology roadmap for the transition to sustainable and competitive electric aircraft systems. This article originates from the GENESIS research and describes various options for ground power supply at a regional airport. Potential solutions for airport infrastructure with a short (2030), medium (2040), and long (2050) time horizon are proposed. In addition to the environmental and conservation benefi...
Post a Comment
Read more

Occipital Dermal Sinus Tract Causing Craniospinal Infection: A Review | Chapter 13 | New Visions in Medicine and Medical Science Vol. 4

  Dermal sinus is a rare congenital condition characterized by a pathological tract connecting the skin to deeper tissues of the central nervous system, potentially leading to severe infectious complications. It arises from a failure in the separation of ectodermal layers during early gestation. Diagnosing dermal sinus tract in newborns requires a careful physical examination, focusing on midline dimples in the occipital region associated with cutaneous abnormalities like hairy nevus or hyperpigmentation. The presence of drainage, abnormal hair distribution, or localized swelling may indicate a sinus tract. Regular examination for dimples or sinuses is recommended for infants and children with recurrent meningitis or infections. Early detection is crucial to prevent severe complications like meningitis, with Staphylococcus aureus being a common causative organism. Neuroradiological studies, including computed tomography (CT) scan and magnetic resonance imaging (MRI), with histopath...
Post a Comment
Read more

Alkali Element Modification of Glucose Molecules as a Method to Dissolve Cancer Cells | Chapter 12 | New Visions in Medicine and Medical Science Vol. 4

  The present study highlights about alkali element modification of glucose molecules as a method to dissolve cancer cells. The central regulation of the mechanisms governing cell proliferation has little effect on cancer cells. Cancer cells are entirely independent of the central command and divide and proliferate on their own, making it challenging to activate their response mechanism. Precisely, this is the reason why they are at risk to the health of humans and/or any biological entities. Instead of trying to reconnect the central command of the growth control mechanism to cancer cells that are already out of the range, we present a method of using the cancer cell’s own irresponsive and uncontrolled growth mechanism to their disadvantage and destroy the cancer cells. We found that this is achievable in an atomic/molecular level study of the glucose molecule, which is the primary food source used for growth and energy generation by all cells in the body, including the cancer cel...
Post a Comment
Read more