The metric derivative of set-valued functions
-
Mohamad Muslikh
,
Adem Kilicman
,
Siti Hasana bt Sapar
Abstract
In this article, we introduce the notion of “metrically differentiable” for set-valued functions. By using this notion, it is shown that each Lipschitz set-valued function is differentiable almost everywhere. Its relationship to the differentiation in the sense of Hukuhara and its generalizations are also discussed.
Acknowledgements
The authors are very grateful to the referees for their useful comments that improve the manuscript.
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Meromorphic function sharing a small function with a homogeneous differential polynomial
- On generalized quasi-Einstein manifolds
- On Green’s function of the Robin problem for the Poisson equation
- Moment functions on hypergroup joins
- Sparse reconstruction with multiple Walsh matrices
- On certain equations in semiprime rings and standard operator algebras
- Derivatives of meromorphic functions sharing two sets with least cardinalities
- The metric derivative of set-valued functions
- The relativistic Enskog equation near the vacuum in the Robertson–Walker space-time
Artikel in diesem Heft
- Frontmatter
- Meromorphic function sharing a small function with a homogeneous differential polynomial
- On generalized quasi-Einstein manifolds
- On Green’s function of the Robin problem for the Poisson equation
- Moment functions on hypergroup joins
- Sparse reconstruction with multiple Walsh matrices
- On certain equations in semiprime rings and standard operator algebras
- Derivatives of meromorphic functions sharing two sets with least cardinalities
- The metric derivative of set-valued functions
- The relativistic Enskog equation near the vacuum in the Robertson–Walker space-time
