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Shape preserving approximation using convex smooth piecewise polynomials for functions in $L_p$ quasi normed spaces | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 13، شماره 1، خرداد 2022، صفحه 3363-3370 اصل مقاله (424.22 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.6096 | ||
| نویسندگان | ||
| Iktifa Diaa Jaleel* 1؛ Eman Samir Bhaya2 | ||
| 1Mathematics Department, College of Education for Pure Sciences, University of Babylon, Iraq | ||
| 2Mathematics Department, College of Education for pure Sciences, University of Babylon, Babylon, Iraq | ||
| تاریخ دریافت: 13 اردیبهشت 1400، تاریخ بازنگری: 16 تیر 1400، تاریخ پذیرش: 22 مهر 1400 | ||
| چکیده | ||
| Many papers used the algebraic polynomials to approximate functions in ${{L}}_{{p}}$ space for $0<p<1$. Few are introduced for the convex algebraic polynomials best approximation. But no one proves direct Theorems for constrained convex approximation using smooth interpolatory piecewise polynomials for functions in ${{L}}_{{p}}$, $0<p<1$. That is what we shall introduce here. | ||
| کلیدواژهها | ||
| $L_p$-space؛ piecewise؛ convex approximation؛ derivative | ||
| مراجع | ||
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[1] R.A. DeVore and G.G. Lorentz, Constructive Approximation, Grundlehren Math. Wiss. [Fundam. Principles Math. Sci.], vol. 303 Springer-Verlag, Berlin 1993. [2] K.A. Kopotun, Pointwise and uniform estimates for convex approximation of functions by algebraic polynomial, Constr. Approx. 10 (1994) 153–178. [3] D. Leviatan and I.A. Shevchuk, Monotone approximation estimates involving the third modulus of smoothness, Approx. Theory IX, Vol. I. (Nashville, TN, 1998) Innov. Appl. Math. Vanderbilt Univ. Press Nashville, (1998) 223–230. [4] L.P. Yushchenko, On one counterexample in convex approximation, Ukrain. Math. J. 52(12) (2000) 1956–1963. [5] A.V. Bondarenko and A.V. Prymak, Negative results in shape-preserving higher-order approximations, Mat. Zametki 76 (2004) 6 812–823. [6] K.A. Kopotun, Interpolatory estimates for convex piecewise polynomial approximation, J. Math. Anal. Appl. 474(1) (2019) 467–479. [7] H.H. Gonska, D. Leviatan, I.A. Shevchuk and H.-J. Wenz, Interpolatory pointwise estimates for polynomial approximations, Constr. Approx. 16 (2000) 603–629. [8] K.A. Kopotun, D. Leviatan, A. Prymak and I.A. Shevchuk, Uniform and pointwise shape preserving approximation by algebraic polynomials, Surv. Approx. Theory 6 (2011) 24–74. [9] T.O. Petrova, A counterexample to convex interpolation approximation, Pr. Inst. Mat. Nats. Akad. Nauk Ukr. Mat. Zastos 35 (2002): 107–112. [10] R.A. DeVore and X.M. Yu, Pointwise estimates for monotone polynomial approximation, Constr. Approx. 1 (1985) 323–331. [11] D. Leviatan, Pointwise estimates for convex polynomial approximation, Proc. Amer. Math. Soc. 98(3)(1986) 471–474. [12] X.M. Yu, Pointwise estimates for convex polynomial approximation, Approx. Theory Appl. 1 4 (1985) 65–74. [13] J.D. Cao and H.H. Gonska, Pointwise estimates for higher order convexity preserving polynomial approximation, J. Aust. Math. Soc. Ser. B 36(2) (1994) 213–233. [14] K.A. Kopotun, D. Leviatan and I.A. Shevchuk, Interpolatory pointwise estimates for monotone polynomial approximation, J. Math. Anal. Appl. 459(2) (2018) 1260–1295. [15] G.A. Dzyubenko, D. Leviatan and I.A. Shevchuk, Pointwise estimates of coconvex approximation, Jaen J. Approx. 6 (2014) 261–295. [16] K. A. Kopotun, D. Leviatan, I.L. Petrova and I.A. Shevchuk, Interpolatory pointwise estimates for convex polynomial approximation, Acta Math. Hungar. 163(1) (2020) 85–117. | ||
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