Results 1 to 10 of about 11,568,694 (339)
Bounded analytic functions [PDF]
Bulletin of the American Mathematical Society, 1950 Z. Nehari
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On New Extensions of Hermite-Hadamard Inequalities for Generalized Fractional Integrals [PDF]
Sahand Communications in Mathematical Analysis, 2021 In this paper, we establish some Trapezoid and Midpoint type inequalities for generalized fractional integrals by utilizing the functions whose second derivatives are bounded .
Huseyin Budak +2 more
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On Some New Extensions of Inequalities of Hermite-Hadamard Type for Generalized Fractional Integrals [PDF]
Sahand Communications in Mathematical Analysis, 2022 In this paper, we establish some inequalities for generalized fractional integrals by utilizing the assumption that the second derivative of $\phi (x)=\varpi \left( \frac{\kappa _{1}\kappa _{2}}{\mathcal{\varkappa }}\right) $ is bounded.
Huseyin Budak +2 more
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Constraining Logits by Bounded Function for Adversarial Robustness [PDF]
IEEE International Joint Conference on Neural Network, 2020 We propose a method for improving adversarial robustness by addition of a new bounded function just before softmax. Several studies hypothesize that small logits (inputs of softmax) by logit regularization contributes to adversarial robustness of deep ...
Sekitoshi Kanai +4 more
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Bounds of the Mertens Functions [PDF]
Advances in Dynamical Systems and Applications, 2020 In this paper we derive new properties of Mertens function and discuss about a likely upper bound of the absolute value of the Mertens function √log(𝑥!) > |𝑀(𝑥)| when 𝑥 > 1. Using this likely bound we show that we have a sufficient condition to prove the Riemann Hypothesis.
Darrell Cox +2 more
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Enhanced bounds for Riemann-Liouville fractional integrals: Novel variations of Milne inequalities
AIMS Mathematics, 2023 In this research article, we present novel extensions of Milne type inequalities to the realm of Riemann-Liouville fractional integrals. Our approach involves exploring significant functional classes, including convex functions, bounded functions ...
Hüseyin Budak, Abd-Allah Hyder
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On functions of bounded variation [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 2016 AbstractThe recently introduced concept of ${\mathcal D}$-variation unifies previous concepts of variation of multivariate functions. In this paper, we give an affirmative answer to the open question from [20] whether every function of bounded Hardy–Krause variation is Borel measurable and has bounded ${\mathcal D}$-variation.
Aistleitner, Christoph +3 more
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On function spaces related to some kinds of weakly sober spaces
AIMS Mathematics, 2022 In this paper, we mainly study function spaces related to some kinds of weakly sober spaces, such as bounded sober spaces, $ k $-bounded sober spaces and weakly sober spaces.
Xiaoyuan Zhang, Meng Bao, Xiaoquan Xu
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Universal Function Approximation by Deep Neural Nets with Bounded Width and ReLU Activations [PDF]
Mathematics, 2017 This article concerns the expressive power of depth in neural nets with ReLU activations and a bounded width. We are particularly interested in the following questions: What is the minimal width w min ( d ) so that ReLU nets of width w min ( d ) (and ...
Boris Hanin
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Note on composition of entire functions and bounded $L$-index in direction
Математичні Студії, 2021 We study the following question: ``Let $f\colon \mathbb{C}\to \mathbb{C}$ be an entire function of bounded $l$-index, $\Phi\colon \mathbb{C}^n\to \mathbb{C}$ an be entire function, $n\geq2,$ $l\colon \mathbb{C}\to \mathbb{R}_+$ be a continuous function ...
A. I. Bandura, O. B. Skaskiv, T. M. Salo
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