In this manuscript, we propose a Polya distribution-based generalization of lambda-Bernstein operators. We establish some fundamental results for convergence as well as order of approximation of the proposed operators...
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In this manuscript, we propose a Polya distribution-based generalization of lambda-Bernstein operators. We establish some fundamental results for convergence as well as order of approximation of the proposed operators. We present theoretical result and graph to demonstrate the proposed operator's intriguing ability to interpolate at the interval's end points. In order to illustrate the convergence of proposed operators as well as the effect of changing the parameter "mu," we provide a variety of results and graphs as our paper's conclusion.
In this paper, we introduce a novel extension of the Bernstein-Kantorovich-Stancu type operator of degree n with the help of multiple shape parameters. Voronovskaja and Gruss-Voronovskaja type approximation theorems a...
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In this paper, we introduce a novel extension of the Bernstein-Kantorovich-Stancu type operator of degree n with the help of multiple shape parameters. Voronovskaja and Gruss-Voronovskaja type approximation theorems are examined via Ditzian-Totik moduli of smoothness. We investigate basic statistical convergence properties with respect to a non-negative regular summability matrix. Moreover, using Ditzian-Totik moduli, local and global approximation properties associated to the proposed operator have been established. Finally, several illustrative examples are presented to demonstrate the efficiency, applicability and validity of the operator. The graphical and numerical results verify that the proposed operator gives better approximation as well as expand the previous Bernstein-Kantorovich type modifications including single parameter.
In the present paper, we construct a new class of positive linear lambda-Bernstein operators based on (p, q)-integers. We obtain a Korovkin type approximation theorem, study the rate of convergence of these operators ...
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In the present paper, we construct a new class of positive linear lambda-Bernstein operators based on (p, q)-integers. We obtain a Korovkin type approximation theorem, study the rate of convergence of these operators by using the conception of K-functional and moduli of continuity, and also give a convergence theorem for the lipschitz continuous functions.
Two different proofs for an inf-sup type representation formula (minimax formula) of the additive eigenvalues corresponding to first-order Hamilton-Jacobi equations are given for quasiconvex (level-set convex) Hamilto...
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Two different proofs for an inf-sup type representation formula (minimax formula) of the additive eigenvalues corresponding to first-order Hamilton-Jacobi equations are given for quasiconvex (level-set convex) Hamiltonians not necessarily convex. The first proof, which is similar to known proofs for convex Hamiltonians, invokes a Jensen-like inequality for quasiconvex functions instead of the standard Jensen's inequality. The second proof is completely different with elementary calculations. It is based on the convergence of derivatives of mollified lipschitz continuous functions whose proof is also given. These methods also relate to an approximation problem of viscosity solutions.
We propose a new approach to vague convergence of measures based on the general theory of boundedness due to Hu (1966). The article explains how this connects and unifies several frequently used types of vague converg...
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We propose a new approach to vague convergence of measures based on the general theory of boundedness due to Hu (1966). The article explains how this connects and unifies several frequently used types of vague convergence from the literature. Such an approach allows one to translate already developed results from one type of vague convergence to another. We further analyze the corresponding notion of vague topology and give a new and useful characterization of convergence in distribution of random measures in this topology. (C) 2019 Elsevier B.V. All rights reserved.
We demonstrate that the Fourier partial sums of a lipschitzcontinuous function on the two-dimensional special unitary group converge uniformly to the function. (C) 2017 Elsevier Inc. All rights reserved.
We demonstrate that the Fourier partial sums of a lipschitzcontinuous function on the two-dimensional special unitary group converge uniformly to the function. (C) 2017 Elsevier Inc. All rights reserved.
A direct application of Zorn's Lemma gives that every lipschitz map f : X subset of Q(p)(n) -> Q(p)(l) has an extension to a lipschitz map (f) over tilde : Q(p)(n) -> Q(p)(l). This is analogous, but more eas...
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A direct application of Zorn's Lemma gives that every lipschitz map f : X subset of Q(p)(n) -> Q(p)(l) has an extension to a lipschitz map (f) over tilde : Q(p)(n) -> Q(p)(l). This is analogous, but more easy, to Kirszbraun's Theorem about the existence of lipschitz extensions of lipschitz maps S subset of R-n -> R-l. Recently, Fischer and Aschenbrenner obtained a definable version of Kirszbraun's Theorem. In the present paper, we prove in the p-adic context that (f) over tilde can be taken definable when f is definable, where definable means semi-algebraic or subanalytic (or, some intermediary notion). We proceed by proving the existence of definable, lipschitz retractions of Q(p)(n) to the topological closure of X when X is definable.
In this paper, we introduce a new type lambda-Bernstein operators with parameter lambda epsilon[- 1, 1], we investigate a Korovkin type approximation theorem, establish a local approximation theorem, give a convergenc...
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In this paper, we introduce a new type lambda-Bernstein operators with parameter lambda epsilon[- 1, 1], we investigate a Korovkin type approximation theorem, establish a local approximation theorem, give a convergence theorem for the lipschitz continuous functions, we also obtain a Voronovskaja-type asymptotic formula. Finally, we give some graphs and numerical examples to show the convergence of B-n,B-lambda(f;x) to f (x), and we see that in some cases the errors are smaller than B-n(f) to f.
In this paper, we introduce a new kind of modified Bernstein-Schurer operators based on the concept of (p, q)-integers. We investigate statistical approximation properties, establish a local approximation theorem, giv...
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In this paper, we introduce a new kind of modified Bernstein-Schurer operators based on the concept of (p, q)-integers. We investigate statistical approximation properties, establish a local approximation theorem, give a convergence theorem for the lipschitz continuous functions, we also obtain a Voronovskaja-type asymptotic formula. Next, we construct the bivariate operators and get some convergence properties. Finally, we give some graphs to illustrate the convergence properties of operators to some functions.
Let F:R-N -> R-N be a locally lipschitzcontinuous function. We prove that F is a global homeomorphism or only injective, under suitable assumptions on the subdifferential partial derivative F(x). We use variationa...
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Let F:R-N -> R-N be a locally lipschitzcontinuous function. We prove that F is a global homeomorphism or only injective, under suitable assumptions on the subdifferential partial derivative F(x). We use variational methods, nonsmooth inverse function theorem and extensions of the Hadamard-Levy Theorem. We also address questions on the Markus-Yamabe conjecture.
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