Limit, Continuity, Differentiability

Sardar, Rupam

ISBN 10: 6208434203 / ISBN 13: 9786208434205

Published by LAP Lambert Academic Publishing, 2025

PRINT ON DEMAND. Seller Inventory # 18404100932

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.

Bibliographic Details

Title: Limit, Continuity, Differentiability
Publisher: LAP Lambert Academic Publishing
Publication Date: 2025
Binding: Soft cover
Condition: New