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Ostrowski type inequalities for sets and functions of bounded variation [PDF]

Journal of Inequalities and Applications, 2017
In this paper we obtain sharp Ostrowski type inequalities for multidimensional sets of bounded variation and multivariate functions of bounded variation.
Oleg V Kovalenko
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Bounded Variation Separates Weak and Strong Average Lipschitz [PDF]

Entropy
We closely examine a recently introduced notion of average smoothness. The latter defined a weak and strong average-Lipschitz seminorm for real-valued functions on general metric spaces.
Ariel Elperin, Aryeh Kontorovich
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Capacity and the Corresponding Heat Semigroup Characterization from Dunkl-Bounded Variation

Fractal and Fractional, 2021
In this paper, we study some important basic properties of Dunkl-bounded variation functions. In particular, we derive a way of approximating Dunkl-bounded variation functions by smooth functions and establish a version of the Gauss–Green Theorem.
Xiangling Meng, Yu Liu, Xiangyun Xie
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BOUNDED VARIATION ON THE SIERPIŃSKI GASKET

Fractals, 2022
Under certain continuity conditions, we estimate upper and lower box dimensions of the graph of a function defined on the Sierpiński gasket. We also give an upper bound for Hausdorff dimension and box dimension of the graph of a function having finite energy.
Verma, S., Sahu, A.
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Nonlocal boundary value problems with BV-type data

Electronic Journal of Qualitative Theory of Differential Equations, 2020
In this paper we present some existence and uniqueness results for solutions of second order boundary value problems, which are functions of bounded variation along with their derivatives.
Jürgen Appell, Daria Bugajewska, Simon Reinwand   +2 more
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Variational Inference with Holder Bounds

CoRR, 2021
The recent introduction of thermodynamic integration techniques has provided a new framework for understanding and improving variational inference (VI). In this work, we present a careful analysis of the thermodynamic variational objective (TVO), bridging the gap between existing variational objectives and shedding new insights to advance the field. In
Junya Chen, Danni Lu, Zidi Xiu, Ke Bai 0001, Lawrence Carin, Chenyang Tao   +5 more
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Some convergence results for nonlinear Baskakov-Durrmeyer operators

Karpatsʹkì Matematičnì Publìkacìï, 2023
This paper is an introduction to a sequence of nonlinear Baskakov-Durrmeyer operators $(NBD_{n})$ of the form \[ (NBD_{n})(f;x) =\int_{0}^\infty K_{n}(x,t,f(t))\,dt \] with $x\in [0,\infty)$ and $n\in\mathbb{N}$.
H.E. Altin
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Variation Inequalities for the Hardy-Littlewood Maximal Function on Finite Directed Graphs

Mathematics, 2022
In this paper, the authors establish the bounds for the Hardy-Littlewood maximal operator defined on a finite directed graph G→ in the space BVp(G→) of bounded p-variation functions.
Feng Liu, Xiao Zhang
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On Bi-Dimensional Second µ-Variation

Demonstratio Mathematica, 2014
In this paper, we present a generalization of the notion of bounded slope variation for functions defined on a rectangle Iba in ℝ2. Given a strictly increasing function µ-defined in a closed real interval, we introduce the class BVµ,2 (Iba ), of ...
Ereú Jurancy, Giménez José, Merentes Nelson   +2 more
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Functions of Bounded κφ-Variation in the Sense of Riesz-Korenblum

Journal of Function Spaces and Applications, 2013
We present the space of functions of bounded κφ-variation in the sense of Riesz-Korenblum, denoted by κBVφ[a,b], which is a combination of the notions of bounded φ-variation in the sense of Riesz and bounded κ-variation in the sense of Korenblum ...
Mariela Castillo, Sergio Rivas, María Sanoja, Iván Zea   +3 more
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