تقرير
Generalized Hukuhara directional differentiability of interval-valued functions on Riemannian manifolds
العنوان: | Generalized Hukuhara directional differentiability of interval-valued functions on Riemannian manifolds |
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المؤلفون: | Bhat, Hilal Ahmad, Iqbal, Akhlad |
سنة النشر: | 2022 |
المجموعة: | Mathematics |
مصطلحات موضوعية: | Mathematics - Optimization and Control, Mathematics - Differential Geometry |
الوصف: | In this paper, we show that generalized Hukuhara directional differentiability of an interval-valued function (IVF) defined on Riemannian manifolds is not equivalent to the directional differentiability of its center and half-width functions and hence not to its end point functions. This contrasts with S.-L. Chen's \cite{chen} assertion which says the equivalence holds in terms of endpoint functions of an IVF which is defined on a Hadamard manifold. Additionally, the paper addresses some inaccuracies made by the author which arise when assuming the convexity of a function at a single point in its domain. In light of these arguments, the paper presents some basic results that relate to both the convexity and directional differentiability of an IVF. |
نوع الوثيقة: | Working Paper |
URL الوصول: | http://arxiv.org/abs/2212.04541 |
رقم الأكسشن: | edsarx.2212.04541 |
قاعدة البيانات: | arXiv |
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