On Approximation Properties of Multivariate Class of Nonlinear Singular Integral Operators

In the present paper, we study the pointwise approximation of nonlinear multivariate singular integral operators having convolution type kernels of the form:T (f; x) =ZDK (t x; f(t)) dt; x 2 D; 2 ;where D =ni=1 hai; bii is open, semi-open or closed multidimensional arbitrarybounded box in Rn or D = Rn and is non-empty the set of non-negativeindices, at a -generalized Lebesgue point of f 2 Lp(D): Also, we investigatethe corresponding rates of convergences at this point

A Class of Integral Operators that Fix Exponential Functions

AbstractIn this paper we introduce a general class of integral operators that fix exponential functions, containing several recent modified operators of Gauss–Weierstrass, or Picard or moment type operators. Pointwise convergence theorems are studied, using a Korovkin-type theorem and a Voronovskaja-type formula is obtained

A new approach to nonlinear singular integral operators depending on three parameters

In this paper, we present some theorems on weighted approximation by two dimensional nonlinear singular integral operators in the following form: Tλ(f;x,y)=∬R2Kλ(t−x,s−y,f(t,s))dsdt,(x,y)∈R2,λ∈Λ,$${T_\lambda }(f;x,y) = \iint\limits_{{\mathbb{R}^2}}K_\lambda {(t - x,s - y,f(t,s))dsdt,\;(x,y) \in {\mathbb{R}^2},\lambda \in \Lambda ,}$$ where Λ is a set of non-negative numbers with accumulation point λ0

ON SINGULAR INTEGRAL OPERATORS INVOLVING POWER NONLINEARITY

Uysal, Gumrah/0000-0001-7747-1706WOS: 000419023400002In the current manuscript, we investigate the pointwise convergence of the singular integral operators involving power non linearity given in the following form: T-lambda(f;x) = integral(b)(a) Sigma(n)(m=1) f(m)(t)K-lambda,K-m(x,t)dt, lambda epsilon Lambda, x epsilon (a, b), where A is an index set consisting of the non-negative real numbers, and n >= 1 is a finite natural number, at mu-generalized Lebesgue points of integrable function f epsilon L-1 (a, b). Here, f(m) denotes m - th power of the function f and (a, b) stands for arbitrary bounded interval in or I itself. We also handled the indicated problem under the assumption f epsilon L-1 (N