A SUMMABILITY METHOD FOR FOURIER SERIES OF FUNCTIONS OF GENERALIZED BOUNDED VARIATION
Analysis, 1997The authors presented an interesting summability method which sums the Fourier series of a function of \(\Lambda\)-bounded variation everywhere to \({1\over 2}(f(x+)+ f(x-))\) and uniformly on any closed interval of points of continuity. Their method is given by a kernel function, in terms of the sequence \(\Lambda\), and this method is specific to the
D'Antonio, Lawrence A., Waterman, Daniel
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Gap functions and error bounds for generalized vector variational inequalities
Optimization Letters, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiang-Kai Sun, Yi Chai 0003
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Generalized gap functions and error bounds for generalized variational inequalities
Applied Mathematics and Mechanics, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hu, Yan-hong, Song, Wen
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On a generalization of the class of functions with bounded Mocanu variation
Proceedings of the Indian Academy of Sciences - Section A, 1981The object of this paper is to generalise the well-known class of functions analytic in the unit disc having bounded Mocanu variation. Certain properties of this more general class are investigated using convolution techniques.
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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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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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Convolution functions of several variables with generalized bounded variation
Analysis Mathematica, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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