In the present paper we introduce positive linear operators q−Bernstein Chlodowsky polynomials on a rectangular domain and obtain their Korovkin type approximation properties. The rate of convergence of this generalization is obtained by means of the modulus of continuity, and also by using the K-functional of Peetre. We obtain weighted approximation properties for these positive linear operato...

In the present work, by applying known Bernstein polynomials and their advantageous properties, we establish an efficient iterative algorithm to approximate the numerical solution of fuzzy Fredholm integral equations of the second kind. The convergence of the proposed method is given and the numerical examples illustrate that the proposed iterative algorithm are ‎valid.‎

Some estimates are proved for the generalized Fourier-Bessel transform in the space (L^2) (alpha,n)-index certain classes of functions characterized by the generalized continuity modulus.

We characterize the functions defined on a weighted space, which are uniformly approximated by a sequence of positive linear operators and we obtain the range of the weights which can be used for uniform approximation. We, also, obtain an estimation of the remainder in terms of the usual modulus of continuity. We give particular results for the Szász-Mirakjan and Baskakov operators. Mathematics...

In this paper we define the modified q-Stancu-Beta operators and study the weighted statistical approximation by these operators with the help of the Korovkin type approximation theorem. We also establish the rates of statistical convergence by means of the modulus of continuity and the Lipschitz type maximal function. Our results show that rates of convergence of our operators are at least as ...

Let f be a bounded function on the real line IF!. One may characterize the structural properties off by the modulus of smoothness w(t,f) = sup{lf (4 -f( y)l; x, y E 08, I x y I < t>, and, if w(t) is a continuous nondecreasing function of t > 0 such that w(O) = 0, by the Lipschitz class Lip(w) which is the set of all continuous functions such that su~~<~<i w(t, f)/o(t) < 00. It is possible to ex...

The goal of this paper is to give a form the operator involving generating function Apostol-Genocchi polynomials order α. Applying Korovkin theorem, we arrive at convergence with aid moments and central moments. We determine rate using several tools such as -functional, modulus continuity, second continuity. also type Voronovskaya theorem for estimating error. Moreover, investigate some results...

We prove a general functional limit theorem for mul-tiparameter fractional Brownian motion. The functional law of the iterated logarithm, functional Lévy's modulus of continuity and many other results are its particular cases. Applications to approximation theory are discussed.

The present article deals with the study on approximation properties of well known Sz?sz-Mirakyan operators. We estimate quantitative Voronovskaja type asymptotic formula for Sz?sz-Baskakov operators and difference between hybrid Sz?sz having weights Baskakov basis in terms weighted modulus continuity