Inhomogenous RefinementEquations.
Kantorovic Operators of Second Order.
Kantorovich-Stancu type operators.
King type modification of -Bernstein-Schurer operators
Very recently the -Bernstein-Schurer operators which reproduce only constant function were introduced and studied by C. V. Muraru (2011). Inspired by J. P. King, Positive linear operators which preserve (2003), in this paper we modify -Bernstein-Schurer operators to King type modification of -Bernstein-Schurer operators, so that these operators reproduce constant as well as quadratic test functions and study the approximation properties of these operators. We establish a convergence theorem...
-approximation by the method of integral Meyer-König and Zeller operators
-inverse theorem for modified beta operators.
Lacunary equi-statistical convergence of positive linear operators
In this paper, the concept of lacunary equi-statistical convergence is introduced and it is shown that lacunary equi-statistical convergence lies between lacunary statistical pointwise and lacunary statistical uniform convergence. Inclusion relations between equi-statistical and lacunary equi-statistical convergence are investigated and it is proved that, under some conditions, lacunary equi-statistical convergence and equi-statistical convergence are equivalent to each other. A Korovkin type approximation...
Left general fractional monotone approximation theory
We introduce left general fractional Caputo style derivatives with respect to an absolutely continuous strictly increasing function g. We give various examples of such fractional derivatives for different g. Let f be a p-times continuously differentiable function on [a,b], and let L be a linear left general fractional differential operator such that L(f) is non-negative over a closed subinterval I of [a,b]. We find a sequence of polynomials Qₙ of degree ≤n such that L(Qₙ) is non-negative over I,...
Legendre and Chebyshev Spectral Approximations of Burger's Equation.
Linear Programming and Discrete Polynomial Type Approximation in the L_1 Norm
Lineare Approximation durch komplexe Exponentialsummen.
Lipschitz-Nikolskii constants and asymptotic simultaneous approximation of the Mn-operators. (Short Communication).
Lipschitz-Nikolskii constants and asymptotic simultaneous approximation of the Mn-operators.
Local approximation properties of certain class of linear positive operators via I-convergence
In this study, we obtain a local approximation theorems for a certain family of positive linear operators via I-convergence by using the first and the second modulus of continuities and the elements of Lipschitz class functions. We also give an example to show that the classical Korovkin Theory does not work but the theory works in I-convergence sense.
Local convergence analysis of a modified Newton-Jarratt's composition under weak conditions
A. Cordero et. al (2010) considered a modified Newton-Jarratt's composition to solve nonlinear equations. In this study, using decomposition technique under weaker assumptions we extend the applicability of this method. Numerical examples where earlier results cannot apply to solve equations but our results can apply are also given in this study.
Maximal order for quadratures using n evaluations.
Maximally convergent rational approximants of meromorphic functions
Let f be meromorphic on the compact set E ⊂ C with maximal Green domain of meromorphy , ρ(f) < ∞. We investigate rational approximants of f on E with numerator degree ≤ n and denominator degree ≤ mₙ. We show that a geometric convergence rate of order on E implies uniform maximal convergence in m₁-measure inside if mₙ = o(n/log n) as n → ∞. If mₙ = o(n), n → ∞, then maximal convergence in capacity inside can be proved at least for a subsequence Λ ⊂ ℕ. Moreover, an analogue of Walsh’s...
Minimum Relative Error Approximations for 1/t.
Mixed K-Functionals: A Measure of Smoothness for Blending-type Approximation.
Modifizierte Restgliedabschätzungen für Quadraturformeln.