Aequationes mathematicae

, Volume 90, Issue 6, pp 1129–1145 | Cite as

On Hukuhara’s differentiable iteration semigroups of linear set-valued functions

  • Masoumeh Aghajani
  • Kourosh Nourouzi


In this paper, we investigate the uniform convergence of continuous linear set-valued functions on compact sets. We also consider conditions under which the family of continuous linear extensions of a differential iteration semigroup of continuous linear set-valued functions is a differentiable iteration semigroup. In particular, since the cones and normed spaces are not supposed to be complete our main results generalize some recent results on Hukuhara’s derivative of set-valued functions.


Hukuhara’s derivative Iterations Linear set-valued functions Cauchy problem for a set-valued differential equation Riemann integral for set-valued functions 

Mathematics Subject Classification

Primary 46G05 Secondary 39B12 54C60 


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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceShahid Rajaee Teacher Training UniversityTehranIran
  2. 2.Faculty of MathematicsK. N. Toosi University of TechnologyTehranIran

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