Limit, Continuity, Differentiability - Softcover

Sardar, Rupam

Softcover

ISBN 10: 6208434203 ISBN 13: 9786208434205

Publisher: LAP Lambert Academic Publishing, 2025

Synopsis

We introduce a new type of functions from a soft set to a soft set and study their properties under soft real number setting. Firstly, we investigate some properties of soft real sets. Considering the partial order relation of soft real numbers, we introduce concept of soft intervals. Boundedness of soft real sets is defined, and the celebrated theorems like nested intervals theorem and Bolzano-Weierstrass theorem are extended in this setting. Next, we introduce the concepts of limit, continuity, and differentiability of functions of soft sets. It has been possible for us to study some fundamental results of continuity of functions of soft sets such as Bolzano's theorem, intermediate value property, and fixed point theorem. Because the soft real numbers are not linearly ordered, several twists in the arguments are required for proving those results. In the context of differentiability of functions, some basic theorems like Rolle's theorem and Lagrange's mean value theorem are also extended in soft setting.

Edition details

• Publisher: LAP Lambert Academic Publishing
• Publication date: 2025
• Language: English
• ISBN 10: 6208434203
• ISBN 13: 9786208434205
• Binding: Paperback
• Number of pages: 52