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Real-Valued Lipschitz Functions and Classes of Locally Lipschitz Functions
2023openaire +1 more source
Convexity and generalized second-order derivatives for locally lipschitz functions
Nonlinear Analysis, 2005Given a normed space \(X\) with sphere \(S_{X}\) and a nonempty open subset \(U\) of \(X,\) the author proves that a locally Lipschitz function \(f:X\rightarrow\mathbb{R}\) is convex if and only if for every \(x\in X\) and \(h\in S_{X}\) one has \(f_{+}^{\prime\prime}(x)(h,h)\geq0,\) where \[ f_{+}^{\prime\prime}(x)(u,v)={\lim\inf}_{t\to0}\,\left ...
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Every Convex Function is Locally Lipschitz
The American Mathematical Monthly, 1972openaire +2 more sources
Locally Lipschitz Functions, Cofinal Completeness, and UC Spaces
Journal of Mathematical Analysis and Applications, 2015Gerald Beer, M Isabel Garrido
exaly
On Locally-Lipschitz Quasi-Differentiate Functions in Banach-Spaces
Optimization, 1986Diethard Pallaschke, R Urbański
exaly
Adjuvant Radiation Therapy in Locally Advanced Head and Neck Cancer
Ca-A Cancer Journal for Clinicians, 1983Bhadrasain Vikram
exaly
Where Must Each Member of a Class of Locally Lipschitz Functions be Lipschitz?
2023openaire +1 more source
Proximal Point Method for Minimizing Quasiconvex Locally Lipschitz Functions on Hadamard Manifolds
Nonlinear Analysis: Theory, Methods & Applications, 2012P R Oliveira
exaly