It easy to see that every bounded linear operator is continuous. It is not hard to show that the converse is also true. The notions of bounded and continuous thereby coincide for linear operators acting between normed spaces. It is customary to prefer the terminology bounded linear operator over that of continuous linear operator. The reason for this preference is the fact that the hard part of...

Very recently Jain et al. [4] proposed generalized integrated Baskakov operators Vn,α(f, x), α > 0 and estimated some approximation properties in simultaneous approximation. In the present paper we establish the rate of convergence of these operators and its Bezier variant, for functions which have derivatives of bounded variation.

We study the rate of convergence in simultaneous approximation for the Bézier variant of Szász– Mirakyan–Durrmeyer operators by using the decomposition technique of functions of bounded variation. © 2006 Elsevier Inc. All rights reserved.

Let H be a Hilbert space. For a bounded operator A : H → H its Hilbert space adjoint is an operator A∗ : H → H such that 〈Ax, y〉 = 〈x,A∗y〉 for all x, y ∈ H. We say that A is bounded self adjoint if A = A∗. In this chapter we discussed several results about the spectrum of a bounded self adjoint operator on a Hilbert space. We emphasize that in this chapter A is bounded, there is also a notion o...

The present paper deals with the approximation of Bézier variants of Baskakov-Kantorovich operators V ∗ n,α in the case 0 < α < 1. Pointwise approximation properties of the operators V ∗ n,α are studied. A convergence theorem of this type approximation for locally bounded functions is established. This convergence theorem subsumes the approximation of functions of bounded variation as a special...

In the present paper, we introduce the Durrmeyer variant of Baskakov-Bezier operators Bn,α(f, x), which is the modified form of Baskakov-Beta operators. Here we obtain an estimate on the rate of convergence of Bn,α(f, x) for functions of bounded variation in terms of Chanturiya’s modulus of variation. In the end we also propose an open problem for the readers.

$K$-frames which are generalization of frames on Hilbert spaces‎, ‎were introduced‎ ‎to study atomic systems with respect to a bounded linear operator‎. ‎In this paper‎, ‎$*$-$K$-frames on Hilbert $C^*$-modules‎, ‎as a generalization of $K$-frames‎, ‎are introduced and some of their properties are obtained‎. ‎Then some relations‎ ‎between $*$-$K$-frames and $*$-atomic systems with respect to a...