This paper studies the integration of inclusion of subdifferentials. Under various verifiable conditions, we obtain that if two proper lower semicontinuous functions f and g have the subdifferential of f included in t...
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This paper studies the integration of inclusion of subdifferentials. Under various verifiable conditions, we obtain that if two proper lower semicontinuous functions f and g have the subdifferential of f included in the gamma-enlargement of the subdifferential of g, then the difference of those functions is gamma-Lipschitz over their effective domain.
Our aim in this article is to study the class of so-called rho-paraconv ex multifunctions from a Banach space X into the subsets of another Banach space Y. These multifunctions are defined in relation with a modulus f...
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Our aim in this article is to study the class of so-called rho-paraconv ex multifunctions from a Banach space X into the subsets of another Banach space Y. These multifunctions are defined in relation with a modulus function rho : X -> [0, +infinity) satisfying some suitable conditions. This class of multifunctions generalizes the class of gamma-paraconvex multifunctions with gamma > 1 introduced and studied by Rolewicz, in the eighties and subsequently studied by A. Jourani and some others authors. We establish some regular properties of graphical tangent and normal cones to paraconvex multifunctions between Banach spaces as well as a sum rule for coderivatives for such class of multifunctions. The use of subdifferential properties of the lower semicontinuous envelope function of the distance function associated to a multifunction established in the present paper plays a key role in this study.
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