On approximation properties of certain non-convolution integral operators

Approximation Properties of Certain Summation Integral Type Operators

n` k ́ 1 k ̇ xk p1` xqn`k , bn,kptq “ 1 Bpn` 1, kq tk ́1 p1` tqn`k`1 . Gupta et al. [12] studied pointwise convergence, an asymptotic formula and error estimation for the operators Bnpf, ̈q. Recently, Govil and Gupta [7] studied some approximation properties for the operators Bnpf, ̈q and estimated local results in terms of modulus of continuity. Generalization of the operators (1.1) with parameter ...

Some Properties for Certain Integral Operators

Abstract. Recently Breaz and Breaz [4] and Breaz et.al[5] introduced two general integral operators Fn and Fα1,...,αn . Considering the classes N(γ), MT(μ, β) and KD(μ, β) we derived some properties for Fn and Fα1,...,αn . Two new subclasses KDFn(μ, β, α1, ..., αn) and KDFα1,...,αn(μ, β, α1, ..., αn) are defined. Necessary and sufficient conditions for a family of functions fj to be in the KDFn...

A note on certain convolution operators

In this note we consider a certain class of convolution operators acting on the Lp spaces of the one dimensional torus. We prove that the identity minus such an operator is nicely invertible on the subspace of functions with mean zero. 2010 Mathematics Subject Classification. Primary 47G10; Secondary 47B34, 26D10.

On the Convexity of Certain Integral Operators

In this paper we consider the classes of starlike functions of order α, convex functions of order α and we study the convexity and α-order convexity for some general integral operators. Several corollaries of the main results are also considered.

Subordination and Super Ordination Results Involving Certain Convolution Operators