The important direction of i-smooth analysis is the investigation of the relation of invariant derivatives with the Sobolev generalized derivative and the generalized derivative of distribution theory
The notion of the invariant derivative i-derivative of nonlinear functionals has been introduced in mathematics, and this in turn developed the corresponding i-smooth calculus of functionals and showed that for linear continuous functionals the invariant derivative coincides with the generalized derivative of the distribution theory
This book intends to introduce this theory to the general mathematics, engineering, and physicist communities.
This is a new direction in mathematics
Until now, i-smooth analysis has been developed mainly to apply to the theory of functional differential equations, and the goal of this book is to present i-smooth analysis as a branch of functional analysis
I-Smooth analysis is the branch of functional analysis that considers the theory and applications of the invariant derivatives of functions and functionals