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Shyam Lal - One of the best experts on this subject based on the ideXlab platform.
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euler hausdorff matrix summability operator and trigonometric Approximation of the conjugate of a function belonging to the generalized lipschitz class
Journal of Inequalities and Applications, 2013Co-Authors: Shyam Lal, Abhishek MishraAbstract:In this paper, three new estimates for the Degree of Approximation of a function ˜ f ,t he conjugate of a function f belonging to classes Lip α and Lip(ξ , r), r ≥ 1, by E (q) · � H summability operator of conjugate series of the Fourier series have been determined. MSC: 42A24; 41A25; 42B05; 42B08
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Approximation of functions belonging to the generalized lipschitz class by c1 np summability method of fourier series
Applied Mathematics and Computation, 2009Co-Authors: Shyam LalAbstract:Abstract In this paper, two new theorems on the Degree of Approximation of the function f ∈ Lip α and f ∈ W ( L r , ξ ( t )) have been established.
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on the Approximation of function belonging to weighted l p xi t class by almost matrix summability method of its fourier series
Tamkang Journal of Mathematics, 2004Co-Authors: Shyam LalAbstract:In this paper, the Degree of Approximation of function belonging to weighted $ W(L^p$, $ \xi(t))$ class by almost matrix summability of its Fourier series has been determined. The main theorem improves all the previously known theorems in this line of work.
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Degree of Approximation of conjugate of lip alpha p function by c 1 e 1 means of conjugate of a fourier series
Tamkang Journal of Mathematics, 2002Co-Authors: Shyam Lal, Prem Narain SinghAbstract:An estimate of Degree of Approximation of conjugates of Lip$ (\alpha, p)$ functions by ($ C$,1) ($ E$,1) product means of conjugate series of a Fourier Series is obtained.
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Degree of Approximation of conjugate of a function belonging to lip ξ t p class by matrix summability means of conjugate fourier series
International Journal of Mathematics and Mathematical Sciences, 2001Co-Authors: Shyam Lal, H K NigamAbstract:We determine the Degree of Approximation of conjugate of a function belonging to Lip(ξ(t), p) class by matrix summability means of a conjugate series of a Fourier series. 2000 Mathematics Subject Classification. 42B05, 42B08. 1. Introduction. Bernstein (2), Alexits (1), Sahney and Goel (14), and Chandra (4) have determined the Degree of Approximation of a function belonging to Lip α by (C, 1), (C, δ), (N, pn), and (N,p n) means of its Fourier series. Working in the same direction Sahney and Rao (15) and Khan (6) have studied the Degree of approxima- tion of functions belonging to Lip(α, p) by (N, pn) and (N,p,q) means, respectively. The (N,p,q) summability reduces to (N, pn) summability for qn = 1 for all n, and to (N,q n) means when pn = 1 for all n. After quite a good amount of work on Degree of Approximation of function by different summability means of its Fourier series, for the first time in 1981, Qureshi (12, 13) discussed the Degree of Approximation of conjugate of a function belonging to Lip α and Lip(α, p) by (N, pn) means of conju- gate Fourier series. But nothing seems to have been done so far to obtain the Degree of Approximation of conjugate of a function belonging to Lip(ξ(t), p) class by matrix means of conjugate Fourier series. The Lip(ξ(t), p) class is a generalization of Lip α and Lip(α, p). Matrix means includes as special cases the method of (C, 1), (C, δ), (N, pn), (N,p n), and (N,p,q) means. In an attempt to make an advance study in this direction, we, in this paper, establish a theorem on Degree of Approximation of con- jugate of a function of Lip(ξ(t), p) class by matrix summability means of conjugate series of a Fourier series then both the results of Qureshi (12, 13) come out as partic- ular cases of our theorem.
Rajesh Tailor - One of the best experts on this subject based on the ideXlab platform.
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ratio cum product estimator of finite population mean in double sampling for stratification
Journal of Reliability and Statistical Studies, 2014Co-Authors: Rajesh Tailor, Hilal A. LoneAbstract:In this paper a class of ratio-cum-product estimator of population mean using auxiliary information is suggested in double sampling for stratification with their properties. The bias and mean squared error of the suggested estimator is obtained up to the first Degree of Approximation. The suggested estimator has been compared with ratio and product estimators given by Ige and Tripathi (1987) and usual unbiased estimator of population mean in double sampling for stratification. Asymptotic optimum estimator is identified. Estimator based on estimated optimum value is also obtained. An empirical study has been carried out to assess the performance of the suggested estimator.
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Separate Ratio-type Estimators of Population Mean in Stratified Random Sampling
Journal of Modern Applied Statistical Methods, 2014Co-Authors: Rajesh Tailor, Hilal A. LoneAbstract:Separate ratio-type estimators for population mean with their properties are considered. Some separate ratio-type estimators for population mean using known parameters of auxiliary variate are proposed. The bias and mean squared error of the proposed estimators are obtained up to the first Degree of Approximation. It is shown that the proposed estimators are more efficient than unbiased estimators in stratified random sampling and usual separate ratio estimators under certain obtained conditions. To judge the merits of the proposed estimators, an empirical study was conducted.
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ratio and product type exponential estimators of population mean in double sampling for stratification
Communications for Statistical Applications and Methods, 2014Co-Authors: Rajesh Tailor, Sunil ChouhanAbstract:This paper discusses the problem of estimation of finite population mean in double sampling for stratification. In fact, ratio and product type exponential estimators of population mean are proposed in double sampling for stratification. The biases and mean squared errors of proposed estimators are obtained upto the first Degree of Approximation. The proposed estimators have been compared with usual unbiased estimator, ratio and product estimators in double sampling for stratification. To judge the performance of the proposed estimators an empirical study has been carried out.
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a generalized ratio cum product estimator of finite population mean in stratified random sampling
Communications for Statistical Applications and Methods, 2011Co-Authors: Rajesh Tailor, Balkishan Sharma, Jongmin KimAbstract:This paper suggests a ratio-cum product estimator of a finite population mean using information on the coefficient of variation and the fcoefficient of kurtosis of auxiliary variate in stratified random sampling. Bias and MSE expressions of the suggested estimator are derived up to the first Degree of Approximation. The suggested estimator has been compared with the combined ratio estimator and several other estimators considered by Kadilar and Cingi (2003). In addition, an empirical study is also provided in support of theoretical findings.
B. E. Rhoades - One of the best experts on this subject based on the ideXlab platform.
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2016Co-Authors: B. E. RhoadesAbstract:Abstract. In a recent paper Lal [1] obtained a theorem on the Degree of Approximation of the conjugate of a function belonging to the weighted W (L p; (t)) class using a triangular matrix transform of the conjugate series of the Fourier series representation of the function. The ma-trix involved was assumed to have monotone increasing rows. We establish the same result by removing the monotonicity conditon. Let f be a 2 periodic Lebesgue integrable function, with Fourier series given by f(x) t
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on the Degree of Approximation of functions belonging to a lipschitz class by hausdorff means of its fourier series
Applied Mathematics and Computation, 2011Co-Authors: B. E. Rhoades, Kevser Ozkoklu, Inci AlbayrakAbstract:Abstract In a recent paper Lal and Yadov [4] obtained a theorem on the Degree of Approximation for a function belonging to the Lipschitz class Lip α using the product of the Cesaro and Euler means of order one of its Fourier series. In this paper we extend this result to any regular Hausdorff matrix for the same class of functions.
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on the Degree of Approximation of functions belonging to a lipschitz class by hausdorff means of its fourier series
Tamkang Journal of Mathematics, 2003Co-Authors: B. E. RhoadesAbstract:In a recent paper Lal and Yadav [1] obtained a theorem on the Degree of Approximation for a function belonging to a Lipschitz class using a triangular matrix transform of the Fourier series representation of the function. The matrix involved was the product of $ (C, 1) $, the Cesaro matrix of order one, with $ (E, 1) $, the Euler matrix of order one. In this paper we extend this result to a much wider class of Hausdorff matrices.
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on the Degree of Approximation of the conjugate of a function belonging to the weighted w l p xi t class by matrix means of the conjugate series of a fourier series
Tamkang Journal of Mathematics, 2002Co-Authors: B. E. RhoadesAbstract:In a recent paper Lal [1] obtained a theorem on the Degree of Approximation of the conjugate of a function belonging to the weighted $ W(L^p, \xi(t))$ class using a triangular matrix transform of the conjugate series of the Fourier series representation of the function. The matrix involved was assumed to have monotone increasing rows. We establish the same result by removing the monotonicity conditon.
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on the Degree of Approximation of functions belonging to the weighted l p xi t class by hausdorff means
Tamkang Journal of Mathematics, 2001Co-Authors: B. E. RhoadesAbstract:In this paper we obtain a theorem on the Degree of Approximation of functions belonging to a certain weighted class, using any Hausdorff method with mass function possessing a derivative. This result is a substantial generalization of the theorem of Lal [2].
Naokant Deo - One of the best experts on this subject based on the ideXlab platform.
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stancu kantorovich operators based on inverse polya eggenberger distribution
Applied Mathematics and Computation, 2016Co-Authors: Naokant Deo, Minakshi Dhamija, Dan MiclǎusAbstract:The purpose of this paper is to investigate Approximation properties of Stancu-Kantorovich operators based on inverse Polya-Eggenberger distribution. For these new operators we establish some Approximation properties including uniform convergence, asymptotic formula and Degree of Approximation.
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Degree of Approximation by hybrid operators
Abstract and Applied Analysis, 2013Co-Authors: Naokant Deo, Hee Sun Jung, Ryozi SakaiAbstract:We consider hybrid (Szasz-beta) operators, which are a general sequence of integral type operators including beta function, and we give the Degree of Approximation by these Szasz-beta-Durrmeyer operators.
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on the Degree of Approximation by modified baskakov operators
Lobachevskii Journal of Mathematics, 2011Co-Authors: Naokant Deo, Neha BhardwajAbstract:In the present paper, we give anothermodification of Baskakov operators and study basic properties and Voronovskaya type results for the ordinary Approximation and we also give better error estimate.
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on the Degree of Approximation by new durrmeyer type operators 1
2010Co-Authors: Naokant Deo, Suresh P SinghAbstract:In this paper, we deflne a new kind of positive linear operators and study basic properties as well as Voronovskaya type results. In the last section of this paper we establish the error estimation for simultaneous Approximation in terms of higher order modulus of continuity by using the technique of linear approximating method viz Steklov mean. 2000 Mathematics Subject Classiflcation: 41A30, 41A36.
P N Agrawal - One of the best experts on this subject based on the ideXlab platform.
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Approximation Degree of durrmeyer bezier type operators
Journal of Inequalities and Applications, 2018Co-Authors: P N Agrawal, Serkan Araci, Martin Bohner, Kumari LipiAbstract:Recently, a mixed hybrid operator, generalizing the well-known Phillips operators and Baskakov–Szasz type operators, was introduced. In this paper, we study Bezier variant of these new operators. We investigate the Degree of Approximation of these operators by means of the Lipschitz class function, the modulus of continuity, and a weighted space. We study a direct Approximation theorem by means of the unified Ditzian–Totik modulus of smoothness. Furthermore, the rate of convergence for functions having derivatives of bounded variation is discussed.
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Degree of Approximation for bivariate extension of chlodowsky type q bernsteinstancukantorovich operators
Applied Mathematics and Computation, 2017Co-Authors: Behar Baxhaku, P N AgrawalAbstract:In this paper, we introduce the bivariate generalization of the Chlodowsky-type q-BernsteinStancuKantorovich operators on an unbounded domain and studied the rate of convergence in terms of the Lipschitz class function and complete modulus of continuity. Further, we establish the weighted Approximation properties for these operators. The aim of this paper is to obtain the Degree of Approximation for these bivariate operators in terms of the partial moduli of continuity and the Peetres K- functional. Then, we give generalization of the operators and investigate their Approximations. Furthermore, we show the convergence of the bivariate Chlodowsky-type operators to certain functions by illustrative graphics using Python programming language. Finally, we construct the GBS operators of bivariate Chlodowsky-type q-BernsteinStancuKantorovich and estimate the rate of convergence for these operators with the help of mixed modulus of smoothness.
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Degree of Approximation for bivariate chlodowsky szasz charlier type operators
Results in Mathematics, 2016Co-Authors: P N Agrawal, Nurhayat IspirAbstract:We consider a combination of Chlodowsky polynomials with generalized Szasz operators involving Charlier polynomials. We give the Degree of Approximation for these bivariate operators by means of the complete and partial modulus of continuity, and also by using weighted modulus of continuity. Furthermore, we construct a GBS (Generalized Boolean Sum) operator of bivariate Chlodowsky–Szasz–Charlier type and estimate the order of Approximation in terms of mixed modulus of continuity.
