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Frechet vs. Gateaux Differentiability of Lipschitzian Functions [PDF]
Proceedings of the American Mathematical Society, 1992 Examples have been given of Lipschitzian functions that are Gâteaux-differentiable everywhere, but nowhere Fréchet-differentiable. One such example has been reported, mistakenly, in several papers as having domain in
Gieraltowska-Kedzierska, Maria +1 more
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Mathematics, 2023 A certain class of nonlinear differential equations representing a generalized Van der Pol oscillator is proposed in which we study the behavior of the existing solution.
Safia Meftah +6 more
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On Estimation of the Bullen-Mercer Inequality for Several Classes [PDF]
Sahand Communications in Mathematical AnalysisThis study establishes Bullen-Mercer type inequalities for $h$-convex functions that use Riemann-Liouville fractional operators. The subject matter is a novel fractional version of the existing Bullen-Mercer type inequalities, with simple computations ...
Ahmed Hallouz +2 more
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Smooth Extensions of Lipschitzian Real Functions [PDF]
Proceedings of the American Mathematical Society, 1988 In this short note we point out that any Lipschitzian real function f f defined in a subset K K of a Banach space E E , with span ¯ (K) ≠ E \overline {{\text {span}}} {\text {(K ...
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On Fréchet differentiability of Lipschitzian functions on spaces with gaussian measures [PDF]
Doklady Mathematics, 2007 There is a Borel function \(f\) on \({\mathbb R}^{\infty}\) that is Lipschitz with constant~1 along the Cameron-Martin space such that the set of points of Fréchet differentiablity along \(H\) for \(f\) has \(\gamma\)-measure zero, where \(\gamma\) is the standard Gaussian product measure on~\({\mathbb R}^{\infty}\).
V. Bogachev, E. Priola, N. A. Tolmachev
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Generic differentiability of Lipschitzian functions [PDF]
Transactions of the American Mathematical Society, 1979 It is shown that, in separable topological vector spaces which are Baire spaces, the usual properties that have been introduced to study the local “first order” behaviour of real-valued functions which satisfy a Lipschitz type condition are “generically” equivalent and thus lead to a unique class of “generically smooth” functions.
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Journal of Applied Mathematics, 2015 Consider the variational inequality VI(C,F) of finding a point x*∈C satisfying the property 〈Fx*,x-x*〉≥0 for all x∈C, where C is a level set of a convex function defined on a real Hilbert space H and F:H→H is a boundedly Lipschitzian (i.e., Lipschitzian ...
Caiping Yang, Songnian He
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Mathematical and Computational Applications, 2020 A number of practical problems in science and engineering can be converted into a system of nonlinear equations and therefore, it is imperative to develop efficient methods for solving such equations.
Aliyu Muhammed Awwal +4 more
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Subdifferentials of compactly lipschitzian vector-valued functions [PDF]
Annali di Matematica Pura ed Applicata, 1980 We introduce the concept of compactly lipschitzian functions taking values in a topological vector space F. We show that if F is finite dimensional the Lipschitz functions are compactly lipschitizian. We define the notions of generalized directional derivatives and subdifferentials for such functionsf taking values in an ordered topological vector ...
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Demonstratio Mathematica, 2014 In this paper, we consider the Nemytskii operator (Hf)(t) = h(t, f(t)), generated by a given function h. It is shown that if H is globally Lipschitzian and maps the space of functions of bounded (p,2,α)-variation (with respect to a weight function α ...
Aziz Wadie
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