Summability of multiple Fourier series of functions of bounded generalized variation
Proceedings of the Steklov Institute of Mathematics, 2013Let \(d \geq 1\), \(f\) a function defined on \(R^d\) having period \(2\pi\) in each variable, \(T=[0,2\pi]\) and \(H _j = \{ h_{nj} \}\), \(( j=1,2,\dots ,d, n=1 ,2,\dots d)\) sequences of positive numbers. The paper studies the problem of the convergence of the rectangular partial sums of Fourier series of functions f of bounded \(( H_1, H_2, \dots ...
Goginava, U., Saakyan, A.
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A New Estimate of Double Fourier Coefficients for Functions of Bounded Generalized Variation
Moscow University Mathematics Bulletin, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Convergence Rate of Fourier–Legendre Series of Functions of Generalized Bounded Variation
Mathematical NoteszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bera, R. K., Ghodadra, B. L.
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On certain integral means of functions of generalized bounded variation
Georgian Mathematical Journal, 2019Abstract For certain classes of functions of Λ-bounded variation on [ - π ,
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Functions of Bounded Variation over Non-Smooth Manifolds and Generalized Curvatures
1996The aim of this paper is to describe some recent attempts to introduce a reasonable notion of a function of bounded variation on a non-smooth manifold. This investigation is motivated by a) variational problems on a fixed non-smooth domain; b) problems where the domain is itself to be determined (hence a priori possibly non regular);
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Rate of Convergence of Certain Fourier Series of Functions of Generalized Bounded Variation
Russian MathematicsIn this paper, we discuss the rate of convergence of the rational Fourier series and conjugate rational Fourier series of functions of generalized bounded variation. In particular, well- known Wiener’s and Siddiqi’s theorems for functions of p-bounded variation are proved in more general complete rational orthogonal system.
Bera, R. K., Ghodadra, B. L.
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Conditions for the existence of stieltjes integral of functions of bounded generalized variation
Analysis Mathematica, 1988Necessary and sufficient conditions for the functions \(\phi\) and \(\psi\) are given so that for any function f(x) and g(x) of bounded \(\phi\)- respectively \(\psi\)-variation and having no common breakpoints, the Stieltjes integral \(\int^{2\pi}_{0}f(x)dg(x)\) exists i.e. \(\phi\) and \(\psi\) form an S-pair. Also for functions \(\phi\) and \(\psi\)
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On generalization of uniformly Lipschitz functions and functions of bounded variation
1994Summary: We introduce the space of uniformly Lipschitz functions from \(\mathbb{R}^n\) into \(C(S)\), where \(S\) is quasi-Stonean and functions of bounded variation taking values in a Dedekind complete Riesz space. These are Riesz spaces when ordered by the cone of increasing maps. We then consider order properties of these spaces.
Wickstead, Anthony, Ercan, Z.
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A note on Lagrange interpolation of functions of generalized bounded variation
Approximation Theory and its Applications, 1993Summary: We solve a remainded problem posed by the author [Acta Math. Hung. 53, No. 1/2, 75-84 (1989; Zbl 0683.41001)], whether the following estimate approximation for the class \(f'\in C[-1,1]\cap BV\) by Lagrange interpolation based on the Jacobi abscissas: \(L^{(\alpha,\beta)}_ n(f,x)- f(x)= O(1/n)\) holds, if \(\alpha\neq\beta\alpha, \beta\geq -1\)
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A generalized trapezoid inequality for functions of bounded variation
2000Let \(f\) be a real function of bounded variation on \([a,b]\) . Denote its total variation on that interval by \(\bigvee_{a}^{b}\left( f\right) \) . The authors prove the following inequality \[ \left|\int_{a}^{b}f(t)dt-f(a)(x-a)-f(b)(b-x)\right|\leq \left[ \frac{1}{2} (b-a)+\left|x-\frac{a+b}{2}\right|\right] \bigvee_{a}^{b}\left( f\right) \] for all
Cerone, P. +2 more
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