Khursheed J. Ansari

On (p, q)-analogue of Bernstein operators

In this paper, we introduce a new analogue of Bernstein operators and we call it as (p, q)-Bernstein operators which is a generalization of q-Bernstein operators. We also study approximation properties based on Korovkins type approximation theorem of (p, q)-Bernstein operators and establish some direct theorems. Furthermore, we show comparisons and some illustrative graphics for the convergence of operators to a function.

On a Kantorovich Variant of (p,q) -Szász-Mirakjan Operators

We propose a Kantorovich variant of -analogue of Szasz-Mirakjan operators. We establish the moments of the operators with the help of a recurrence relation that we have derived and then prove the basic convergence theorem. Next, the local approximation and weighted approximation properties of these new operators in terms of modulus of continuity are studied.

Corrigendum to: “Some approximation results by (p, q)-analogue of Bernstein–Stancu operators” [Appl. Math. Comput. 264(2015)392–402]

Abstract In the present paper, we have discussed about Theorem 3.1, Remark 3.1 and Theorem 4.1 studied in our article “Some approximation results by ( p, q )-analogue of Bernstein–Stancu operators” [Appl. Math. Comput. 264 (2015) 392–402]. We give here the correct version of the said Theorem 3.1, Remark 3.1 and Theorem 4.1.

STABILITY OF SOME POSITIVE LINEAR OPERATORS ON COMPACT DISK

Recently, Popa and Rasa [18,19] have shown the (in)stability of some classical operators defined on [0,1] and found best constant when the positive linear operators are stable in the sense of Hyers-Ulam. In this paper we show Hyers-Ulam (in)stability of complex Bernstein-Schurer operators, complex Kantrovich-Schurer operators and Lorentz operators on compact disk. In the case when the operator is stable in the sense of Hyers and Ulam, we find the infimum of Hyers-Ulam stability constants for respective operators.

On the stability of fuzzy set-valued functional equations

We introduce some fuzzy set-valued functional equations, i.e. the generalized Cauchy type (in n variables), the Quadratic type, the Quadratic-Jensen type, the Cubic type and the Cubic-Jensen type fuzzy set-valued functional equations and discuss the Hyers-Ulam-Rassias stability of the above said functional equations. These results can be regarded as an important extension of stability results corresponding to single-valued and set-valued functional equations, respectively.

Generalized ( p , q )

The aim of this paper is to introduce a new generalization of Bleimann-Butzer-Hahn operators by using (p,q)

(p,q)

(p,q)

-Bleimann-Butzer-Hahn operators and some approximation results

-integers which is based on a continuously differentiable function μ on [0,∞)=R+

The Stability of an Affine Type Functional Equation with the Fixed Point Alternative

[0,\infty)=\mathbb{R}_{+}

Some approximation results by (p, q)-analogue of Bernstein-Stancu operators

. We establish the Korovkin type approximation results and compute the degree of approximation by using the modulus of continuity. Moreover, we investigate the shape preserving properties of these operators.