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Non-Linear Operators and Differentiability of Lipschitz Functions
In this work we provide a characterization of distinct types of (linear and non-linear) maps between Banach spaces in terms of the differentiability...
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Comparative Dynamics in Differential Games: A Note on the Differentiability of Solutions
We revisit the assumption of differentiability of solutions with respect to exogenous variables in the differential games literature (e.g., Ling and...
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Continuous Fréchet Differentiability of the Moreau Envelope of Convex Functions on Banach Spaces
It is shown that the Moreau envelope of a convex lower semicontinuous function on a real Banach space with strictly convex dual is Fréchet...
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Differentiability and Local Optimality
In this chapter we give an overview of a variety of facts concerning optimality of a point relative to a neighborhood of it, in terms of ‘local’...
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Existence and Differentiability of Solutions for Nondensely Defined Neutral Integro-Differential Evolution Equations
This paper is concerned with the existence, continuous dependence and differentiability of solutions for a semilinear neutral integro-differential...
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Optimal Control and Directional Differentiability for Elliptic Quasi-Variational Inequalities
We focus on elliptic quasi-variational inequalities (QVIs) of obstacle type and prove a number of results on the existence of solutions, directional...
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Role of Subgradients in Variational Analysis of Polyhedral Functions
Understanding the role that subgradients play in various second-order variational analysis constructions can help us uncover new properties of...
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Necessary Optimality Conditions for Second-Order Local Strict Efficiency for Constrained Nonsmooth Vector Equilibrium Problems
This paper is concerned with primal and dual second-order optimality conditions for the second-order strict efficiency of nonsmooth vector...
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Description of the Class of Strictly Differentiable Finite-State Isometries of the Ring Z2
The condition of strict differentiability strengthens the concept of differentiability, which is naturally applicable to the class of p -adic...
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New interpolation spaces and strict Hölder regularity for fractional abstract Cauchy problem
We know that interpolation spaces in terms of analytic semigroup have a significant role into the study of strict Hölder regularity of solutions of...
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Strict convexity and \(C^1\) regularity of solutions to generated Jacobian equations in dimension two
We present a proof of strict g -convexity in 2D for solutions of generated Jacobian equations with a g -Monge–Ampère measure bounded away from 0....
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Limit, Continuity and Differentiability of Functions
In this chapter, we deal with the concepts of limit, continuity and differentiability of functions. Apart from establishing some of the basic...
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Strict directional solutions in vectorial problems: necessary optimality conditions
We study directional strict efficiency in vector optimization and equilibrium problems with set-valued map objectives. We devise several...
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Local strict singular characteristics II: existence for stationary equations on \({\mathbb {R}}^2\)
The notion of strict singular characteristics is important in the wellposedness issue of singular dynamics on the cut locus of the viscosity...
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Differentiability of distance function and the proximinal condition implying convexity
We establish a necessary and sufficient condition for the differentiability of the distance function generated by a nonempty closed set K in a real...
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Directional Compactness, Approximations and Efficiency Conditions for Nonsmooth Vector Equilibrium Problems with Constraints
In this article, we introduce and study a natural version of the directional compactness, which can be viewed as one of the effective tools for...