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In order to approximate Lebesgue integrable functions on the positive real axis, we propose an integral variant of Baskakov operators. We show that the linear operators so obtained exhibit the quadratic approximation order $ O(n^{-2}) $ for sufficiently large values of $ n. $ [ABSTRACT FROM AUTHOR]

In this paper, we define Bézier variant of generalized Bernstein-Durrmeyer type operators of second order, introduced by Ana et al. Then, we find error estimate in terms of terms of Ditzian Totik modulus of smoothness. Next, we study rate of approximation for larger class function of bounded variation. [ABSTRACT FROM AUTHOR]

Forest fire detection through space-based observations using thermal sensors is in operation since more than one decades. These active fire alerts are generated by using products from MODIS and SNPP--VIIRS satellites and are limited up to identification of active fire locations based on recorded temperature in satellite sensors. However, relation of fire location with forest type map, terrain profile and weather data are required for planning and monitoring of vulnerable areas. An attempt is made to develop online Spatial Decision Support System (SDSS) and spatial model for forest fire risk mapping. The developed SDSS is based on Geospatial Web Service Orchestration (GWSO) workflow which enables forest fire risk alerts and advisories as Web Map Service, Geo SMS and a Geoportal application. User can use this SDSS with minimum technical skills and limited computation resources to generate daily forest fire risk map for fire monitoring and management. [ABSTRACT FROM AUTHOR]

The optimal order of approximation, |Ln f(x) − f(x)| of a linear positive operator Ln f(x) is 1/n and can not be improved however smooth the function may be. We remove the positivity of the Baskakov operator Vn(f ;x) and introduce its three variants VnM,i (f ;x), i = 1,2,3. We prove that the rates of approximation by these operators are improved from the linear order 1/n to quadratic order 1/n² and then to cubic order 1/n³ for sufficiently smooth functions. [ABSTRACT FROM AUTHOR]

We obtain global rates of approximation by qq-Durrmeyer operators Dn,q(f;x) for the functions in the class Lp([0,1]), 1 ≤ p ≤ ∞. First, rates of approximation in terms of the norms of f and f' and in terms of the ordinary modulus of smoothness are obtained. Subsequently, we obtain rates of approximation in terms of the generalized modulus of smoothness ωφ(f,δ). [ABSTRACT FROM AUTHOR]

The Bernstein-Durrmeyer polynomial [Mn(f; t) = (n + 1) k=0 Σ n Pn, k(t) ∫ 0 ¹ Pn, k(u) f (u) du, where Pn, k(t) = (kn) tk(1 - t)n-k, t ϵ [01, 1] defined on LB[0, 1], the space of bounded and integrable functions on [0, 1] were introduced by Durrmeyer [5] and extensively studied by Derriennic [3] and other researchers (see [1]-[3], [5], [6], [8]). It turns out that the order of approximation by these operators is, at best, O(n-1) however smooth the function may be. In order to improve the rate of approximation we consider an iterative combination Tn,k(f; t) of the operators Mn(f; t). This technique was given by Micchelli [9] who first used it to improve the order of approximation by Bernstein polynomials Bn(f; t). In the paper [1] some direct theorems in ordinary and simultaneous approximation for the operators Tn,k(f; t) in the uniform norm, have been established. The paper [10] is a study of some direct results in the Lp- approximation by the operators Tn,k(f; t). The object of the present paper is to study the corresponding inverse theorem in Lp-approximation by the operators Tn,k(f; t). [ABSTRACT FROM AUTHOR]