Related papers: On the paper "statistical approximation by positiv…
The main object of this paper is to construct new Durrmeyer type operators which have better features than the classical one. Some results concerning the rate of convergence and asymptotic formulas of the new operator are given. Finally,…
Using the properties of geometric mean, we shall show for any $0\le \alpha ,\beta \le 1$, \[f\left( A{{\nabla }_{\alpha }}B \right)\le f\left( \left( A{{\nabla }_{\alpha }}B \right){{\nabla }_{\beta }}A \right){{\sharp}_{\alpha }}f\left(…
Let $F^{*}$ be an approximation of a given $(a \times b)$ matrix $F$ derived by methods that are not randomized. We prove that for a given $F$ and $F^{*}$, $H$ and $T$ can be computed by randomized algorithm such that $(HT)$ is an…
This paper has been withdrawn because of serious errors.
The present paper deals with a generalization of the Baskakov operators. Some direct theorems, asymptotic formula and $A$-statistical convergence are established. Our results are based on a $\rho$ function. These results include the…
This note provides a counterexample to a theorem announced in the last part of the paper ''Analysis of direct searches for discontinuous functions'', Mathematical Programming Vol. 133, pp.~299--325, 2012. The counterexample involves an…
In this article, the author provides full details of the proof of the concordance/isotopy problem. The first published proof, [5], accomplished this task only partially since there was an error, see the erratum [6], which damaged the main…
In this paper, we show that the stability analysis in the paper A note on stability of fractional logistic maps, Appl. Math. Lett. 125 (2022) 107787 is incorrect and repeat a proof of a theorem on the convergence of a convolution of the…
The paper has been withdrawn by the author due to a crucial error.
In this paper has been withrawn by the author due the error in the proof of theoem 1.
In this article, for modelling numeral systems, the operator approach, which is introduced in [25], is generalized for a certain case. An example of such numeral systems is introduced and considered.
This paper has been withdrawn by the authors because M. Aschenbrenner pointed out that the proof of theorem 3.1 was incorrect.
This paper has been withdrawn, because of an error in the proof of the main Theorem
In a previous paper I showed how the ideal SLAC derivative and second-derivative operators for an infinite lattice can be obtained in simple closed form in position space, and implemented very efficiently in a stochastic fashion for…
A new type of combinations of Bernstein operators is given in [1]. Here, we introduce another one, which can be used to approximate the functions with singularities. The direct and inverse results of the weighted approximation of this new…
The paper has been withdrawn because the proof of part (b) of the main theorem is incomplete.
We prove a generalization of W.M. Schmidt's theorem related to the Diophantine approximations for a linear form of the type $\alpha_1x_1+\alpha_2x_2 +y$ with {\it positive} integers $x_1,x_2$.
This paper has been withdrawn by the author due to a crucial error.
We present an inequality for tensor product of positive operators on Hilbert spaces by considering the tensor product of operators as words on certain alphabets (i.e., a set of letters). As applications of the operator inequality and by a…
The validity of (1-q) expansion and factorization approximations are analysed in the framework of Tsallis statistics. We employ exact expressions for classical independent systems (harmonic oscillators) by considering the unnormalized and…