Representation of standard Liebchtz functions under a microscope

• Main Authors: Taher Ismail, Hind Saleh
• Format: Article
• Language: Arabic
• Published: College of Education for Pure Sciences 2012-03-01
• Series: مجلة التربية والعلم
• Subjects: standard liebchtz; functions; microscope
• Online Access: https://edusj.mosuljournals.com/article_58986_61111009c6329cfab096e11eb8fa2fa9.pdf

ABSTRACT<br /> The aim of this paper is to provide a representation of a standard lipschitzian functions by mean of a microscope.<br /> More precisely, under certain conditions, the following results have been obtained. <br /> Let be a standard function, and be the shadow of its graph :<br /> (i) If is s-continuous and limited, then is the graph of a continuous function on .<br /> (ii) If is continuous and if is the graph of a function defined on , then is a continuous function.<br /> The standard function is lipschitzian at a neighbourhood of a standard point if and only if is limited under every microscope of power centered at a point or at a point infinitely close to it.<br /> If the standard function is lipschitzian at a neighbourhood of a standard point ,then it's representation under a microscopic of power centered at the point or at a point infinitely close to it, is a graph of a lipschitzian function.