Results 11 to 20 of about 231 (170)

Generalized Csiszár's f-divergence for Lipschitzian functions [PDF]

Mathematical Inequalities & Applications, 2021
We started with the generalization of the Csisz ́ar’s f -divergence. We stated and proved Jensen’s type inequality for L-Lipschitzian functions. The results for commonly used examples of f-divergences, such as the Kullbach-Leibler divergence, the Hellinger divergence, the R ́enyi divergence and χ2 -distance are derived.
Pečarić D., Pečarić J., Pokaz D.
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Clarke Subgradients for Directionally Lipschitzian Stratifiable Functions [PDF]

Mathematics of Operations Research, 2015
Using a geometric argument, we show that under a reasonable continuity condition, the Clarke subdifferential of a semi-algebraic (or more generally stratifiable) directionally Lipschitzian function admits a simple form: The normal cone to the domain and limits of gradients generate the entire Clarke subdifferential.
Dmitriy Drusvyatskiy, Alexander D. Ioffe, Adrian S. Lewis   +2 more
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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, van Vleck, F. S.   +1 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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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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Inequalities for D−Synchronous Functions and Related Functionals

Revista Integración, 2020
We introduce in this paper the concept of quadruple D−synchronous functions which generalizes the concept of a pair of synchronous functions, we establish an inequality similar to Chebyshev inequality and we also provide some Cauchy-Bunyakovsky-Schwarz ...
Silvestru Sever Dragomir
doaj   +1 more source

On Estimation of the Bullen-Mercer Inequality for Several Classes [PDF]

Sahand Communications in Mathematical Analysis
This 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, Bouharket Benaissa, Noureddine Azzouz   +2 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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Newton-type Inequalities for Fractional Integrals by Various Function Classes

Universal Journal of Mathematics and Applications
The authors of the paper examine some Newton-type inequalities for various function classes using Riemann-Liouville fractional integrals. Namely, we establish some Newton-type inequalities for bounded functions by fractional integrals.
Hüseyin Budak, Tingsong Du, Fatih Hezenci   +2 more
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New Approach to Weighted Newton‐Type Inequalities Using Riemann–Liouville Fractional Integrals

Mathematical Methods in the Applied Sciences, Volume 49, Issue 10, Page 11186-11204, 15 July 2026.
ABSTRACT In this investigation paper, we present some weighted inequalities Newton‐type for various classes of functions utilizing Riemann–Liouville fractional integrals. The study begins by introducing a positive weighted function to derive a key integral equality essential for proving the main results.
Rubayyi T. Alqahtani, Hüseyin Budak
wiley   +1 more source