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Given a unital algebra $\mathscr A$ of locally Lipschitz functions defined over a metric measure space $({\mathrm X},{\mathsf d},\mathfrak m)$, we study two associated notions of function of bounded variation and their relations: the space…

Functional Analysis · Mathematics 2026-04-08 Enrico Pasqualetto , Giacomo Enrico Sodini

In this article, we introduce the notion of the Riemann-Liouville fractional integral of set-valued mappings via integrable selections. We establish fundamental properties of this fractional integral, including convexity, boundedness, and…

Dynamical Systems · Mathematics 2025-12-30 Subhash Chandra , Syed Abbas

In arXiv:1306.2914 a method for approximate solution of Sturm-Liouville equations and related spectral problems was presented based on the construction of the Delsarte transmutation operators. The problem of numerical approximation of…

Classical Analysis and ODEs · Mathematics 2016-09-06 Vladislav V. Kravchenko , Sergii M. Torba

We consider abstract operator equations $Fu=y$, where $F$ is a compact linear operator between Hilbert spaces $U$ and $V$, which are function spaces on \emph{closed, finite dimensional Riemannian manifolds}, respectively. This setting is of…

Numerical Analysis · Mathematics 2015-05-28 Nicolas Thorstensen , Otmar Scherzer

This work extends the Mond-Pecaric method to functions with multiple operators as arguments by providing arbitrarily close approximations of the original functions. Instead of using linear functions to establish lower and upper bounds for…

Functional Analysis · Mathematics 2024-07-09 Shih-Yu Chang

Truncating the Fourier transform averaged by means of a generalized Hausdorff operator, we approximate the adjoint to that Hausdorff operator of the given function. We find the formulas for the rate of approximation in various metrics in…

Classical Analysis and ODEs · Mathematics 2019-07-31 Alberto Debernardi , Elijah Liflyand

On a complete, connected, locally compact, non-compact geodesic space $(X,d)$, we assign each compact set a distance-like function. With the help of these functions, we obtain a pseudo-metric on the space of (non-empty) compact subsets of…

Dynamical Systems · Mathematics 2022-02-01 Xiaojun Cui , Liang Jin , Xifeng Su

The aim of this paper is to study variation detracting property and con- vergence in variation of the Bernstein-Durrmeyer modifications of the classical Bernstein operators in the space of functions of bounded variation. These problems are…

Classical Analysis and ODEs · Mathematics 2016-05-16 Ozlem Oksuzer , Harun Karsli , Fatma Tasdelen Yesildal

For self-adjoint operators $A, B$, a bounded operator $J$, and a function $f:\mathbb R\to\mathbb C$ we obtain bounds in quasi-normed ideals of compact operators for the difference $f(A)J-Jf(B)$ in terms of the operator $AJ-JB$. The focus is…

Spectral Theory · Mathematics 2022-01-27 Alexander V. Sobolev

Submodular functions are a fundamental object of study in combinatorial optimization, economics, machine learning, etc. and exhibit a rich combinatorial structure. Many subclasses of submodular functions have also been well studied and…

Data Structures and Algorithms · Computer Science 2013-04-19 Nikhil R. Devanur , Shaddin Dughmi , Roy Schwartz , Ankit Sharma , Mohit Singh

In this paper, we give direct theorems on point wise and global approximation by new variants of Bernstein-Durrmeyer operator, introduced by A.-M. et al.[1].

Classical Analysis and ODEs · Mathematics 2020-05-11 Asha Ram Gairola , Karunesh Kumar Singh

This article is a review of functional $f(R)$ approximations in the asymptotic safety approach to quantum gravity. It mostly focusses on a formulation that uses a non-adaptive cutoff, resulting in a second order differential equation. This…

High Energy Physics - Theory · Physics 2022-10-21 Tim R. Morris , Dalius Stulga

In this work, wavelet-based filtering operators are constructed by introducing a basic function $D(t_1, t_2, t_3)$ using a general wavelet transform. The cardinal orthogonal scaling functions (COSF) provide an idea to derive the standard…

Functional Analysis · Mathematics 2025-06-25 Digvijay Singh , Rahul Shukla , Karunesh Kumar Singh

In this paper, First we have given the modified form of (p,q)-analogues of Bernstein and Bernstein operators [21-23] and then we introduce a new analogue of Bernstein-Kantorovich operators which we call as (p,q)-Bernstein-Kantorovich…

Classical Analysis and ODEs · Mathematics 2016-01-18 M. Mursaleen , Khursheed J. Ansari , Asif Khan

In this paper we focus on efficient implementations of the Multivariate Decomposition Method (MDM) for approximating integrals of $\infty$-variate functions. Such $\infty$-variate integrals occur for example as expectations in uncertainty…

Numerical Analysis · Mathematics 2018-08-06 Alexander D. Gilbert , Frances Y. Kuo , Dirk Nuyens , Grzegorz W. Wasilkowski

The first part of this paper is devoted to introducing an approach to compute the approximate minimum time function of control problems which is based on reachable set approximation and uses arithmetic operations for convex compact sets. In…

Optimization and Control · Mathematics 2016-01-01 Robert Baier , Thuy Thi Thien Le

In this paper we solve the problem of approximating functionals $(\varphi(A)x, f)$ (where $\varphi(A)$ is some function of self-adjoint operator $A$) on the class of elements of a Hilbert space that is defined with the help of another…

Functional Analysis · Mathematics 2017-03-14 Vladyslav Babenko , Yuliya Babenko , Nadiia Kriachko

Our main aim is to investigate the approximation properties for the summation integral type operators in a statistical sense. In this regard, we prove the statistical convergence theorem using well known Korovkin theorem and the degree of…

Functional Analysis · Mathematics 2019-12-24 Rishikesh Yadav , Ramakanta Meher , Vishnu Narayan Mishra

We consider a family of boundary integral operators supported on a collection of parametrically defined bounded Lipschitz boundaries. Consequently, the boundary integral operators themselves also depend on the parametric variables, thus…

Numerical Analysis · Mathematics 2024-07-09 Jürgen Dölz , Fernando Henríquez

The main purpose of this paper is to determine the approximations of Durrmeyer modification of Szasz-Mirakjan operators, defined by Mishra et al. (Boll. Unione Mat. Ital. (2016) 8(4):297-305). We estimate the order of approximation of the…

Functional Analysis · Mathematics 2020-02-14 Rishikesh Yadav , Ramakanta Meher , Vishnu Narayan Mishra