scholarly journals On a special class of modified integral operators preserving some exponential functions

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Gümrah Uysal
Keyword(s):  
Uniform Convergence ◽  
General Class ◽  
Special Class ◽  
Integral Operators ◽  
Quantitative Result ◽  
Kernel Functions ◽  
Exponential Functions ◽  
Type Estimate

<p style='text-indent:20px;'>In the present paper, we consider a general class of operators enriched with some properties in order to act on <inline-formula><tex-math id="M1">\begin{document}$ C^{\ast }( \mathbb{R} _{0}^{+}) $\end{document}</tex-math></inline-formula>. We establish uniform convergence of the operators for every function in <inline-formula><tex-math id="M2">\begin{document}$ C^{\ast }( \mathbb{R} _{0}^{+}) $\end{document}</tex-math></inline-formula> on <inline-formula><tex-math id="M3">\begin{document}$ \mathbb{R} _{0}^{+} $\end{document}</tex-math></inline-formula>. Then, a quantitative result is proved. A quantitative Voronovskaya-type estimate is obtained. Finally, some applications are provided concerning particular kernel functions.</p>

scholarly journals A Class of Integral Operators that Fix Exponential Functions

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
Carlo Bardaro ◽  
Ilaria Mantellini ◽  
Gumrah Uysal ◽  
Basar Yilmaz
Keyword(s):  
General Class ◽  
Pointwise Convergence ◽  
Type Theorem ◽  
Integral Operators ◽  
Exponential Functions ◽  
Convergence Theorems ◽  
Korovkin Type Theorem ◽  
Type Formula

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.

scholarly journals On approximation properties of Baskakov-Schurer-Szász operators preserving exponential functions

Filomat ◽  
2018 ◽  
Vol 32 (15) ◽  
pp. 5433-5440 ◽  
Author(s):  
Övgü Yılmaz ◽  
Murat Bodur ◽  
Ali Aral
Keyword(s):  
Uniform Convergence ◽  
Generating Function ◽  
General Class ◽  
Quantitative Estimate ◽  
Moment Generating Function ◽  
Convergence Result ◽  
Weighted Spaces ◽  
Approximation Properties ◽  
Exponential Functions ◽  
Szász Operators

The goal of this paper is to construct a general class of operators which has known Baskakov-Schurer-Sz?sz that preserving constant and e2ax, a > 0 functions. Also, we demonstrate the fact that for these operators, moments can be obtained using the concept of moment generating function. Furthermore, we investigate a uniform convergence result and a quantitative estimate in consideration of given operator, as well. Finally, we discuss the convergence of corresponding sequences in exponential weighted spaces and make a comparison about which one approximates better between classical Baskakov-Schurer-Sz?sz operators and the recent sequence, too.

scholarly journals Two-weight norm inequalities for fractional integral operators with $A_{\lambda,\infty}$ weights

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Junren Pan ◽  
Wenchang Sun
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Type Estimate ◽  
Norm Inequalities ◽  
Fractional Integral Operators ◽  
New Class ◽  
Formula Type

Abstract In this paper, we introduce a new class of weights, the $A_{\lambda, \infty}$Aλ,∞ weights, which contains the classical $A_{\infty}$A∞ weights. We prove a mixed $A_{p,q}$Ap,q–$A_{\lambda,\infty}$Aλ,∞ type estimate for fractional integral operators.

scholarly journals Lower bounds for tau coefficients and operator norms using composite matrix norms

1987 ◽  
Vol 35 (1) ◽  
pp. 49-57
Author(s):  
Choon Peng Tan
Keyword(s):  
Lower Bounds ◽  
General Class ◽  
Special Class ◽  
Operator Norm ◽  
Composite Matrix ◽  
Operator Norms ◽  
Class Of Matrices ◽  
Matrix Norms

Lower bounds for the tau coefficients and operator norms are derived by using composite matrix norms. For a special class of matrices B, our bounds on ‖B‖p (the operator norm of B induced by the ℓp norm) improve upon a general class of Maitre (1967) bounds for p ≥ 2.

scholarly journals Boundedness for a Class of Singular Integral Operators on Both Classical and Product Hardy Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Chaoqiang Tan
Keyword(s):  
Singular Integral ◽  
Hardy Spaces ◽  
General Class ◽  
Integral Operators ◽  
Singular Integral Operators

We found that the classical Calderón-Zygmund singular integral operators are bounded on both the classical Hardy spaces and the product Hardy spaces. The purpose of this paper is to extend this result to a more general class. More precisely, we introduce a class of singular integral operators including the classical Calderón-Zygmund singular integral operators and show that they are bounded on both the classical Hardy spaces and the product Hardy spaces.

scholarly journals Some fractional proportional integral inequalities

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Gauhar Rahman ◽  
Thabet Abdeljawad ◽  
Aftab Khan ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Integral Operators ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Exponential Functions ◽  
Proportional Integral ◽  
Conformable Derivatives ◽  
Fractional Integrals And Derivatives ◽  
Decreasing Functions

Abstract In the last few years, various researchers studied the so-called conformable integrals and derivatives. Based on that notion some authors used modified conformable derivatives (proportional derivatives) to generate nonlocal fractional integrals and derivatives, called fractional proportional integrals and derivatives, which contain exponential functions in their kernels. Our aim in this paper is to establish some new integral inequalities by utilizing the fractional proportional-integral operators. In fact, certain new classes of integral inequalities for a class of n ($n\in \mathbb{N}$ n ∈ N ) positive continuous and decreasing functions on $[a,b]$ [ a , b ] are presented. The inequalities presented in this paper are more general than the existing classical inequalities.

Weighted inequalities for some integral operators with rough kernels

2014 ◽  
Vol 12 (4) ◽  
Author(s):  
María Riveros ◽  
Marta Urciuolo
Keyword(s):  
Weak Type ◽  
Integral Operators ◽  
Degree Zero ◽  
Weighted Inequalities ◽  
Rough Kernels ◽  
Type Estimate ◽  
Dini Condition ◽  
Weighted Bmo ◽  
Weak Type Estimates ◽  
Invertible Matrices

AbstractIn this paper we study integral operators with kernels $$K(x,y) = k_1 (x - A_1 y) \cdots k_m \left( {x - A_m y} \right),$$ $$k_i \left( x \right) = {{\Omega _i \left( x \right)} \mathord{\left/ {\vphantom {{\Omega _i \left( x \right)} {\left| x \right|}}} \right. \kern-\nulldelimiterspace} {\left| x \right|}}^{{n \mathord{\left/ {\vphantom {n {q_i }}} \right. \kern-\nulldelimiterspace} {q_i }}}$$ where Ωi: ℝn → ℝ are homogeneous functions of degree zero, satisfying a size and a Dini condition, A i are certain invertible matrices, and n/q 1 +…+n/q m = n−α, 0 ≤ α < n. We obtain the appropriate weighted L p-L q estimate, the weighted BMO and weak type estimates for certain weights in A(p, q). We also give a Coifman type estimate for these operators.

Approximation by max-product sampling Kantorovich operators with generalized kernels

2019 ◽  
pp. 1-26 ◽  
Author(s):  
Lucian Coroianu ◽  
Danilo Costarelli ◽  
Sorin G. Gal ◽  
Gianluca Vinti
Keyword(s):  
Uniform Convergence ◽  
Real Axis ◽  
Modulus Of Continuity ◽  
Higher Dimensions ◽  
Jackson Type ◽  
Convergence Properties ◽  
Type Estimate ◽  
Quantitative Estimates ◽  
Uniform Modulus Of Continuity ◽  
Kantorovich Operators

In a recent paper, for max-product sampling operators based on general kernels with bounded generalized absolute moments, we have obtained several pointwise and uniform convergence properties on bounded intervals or on the whole real axis, including a Jackson-type estimate in terms of the first uniform modulus of continuity. In this paper, first, we prove that for the Kantorovich variants of these max-product sampling operators, under the same assumptions on the kernels, these convergence properties remain valid. Here, we also establish the [Formula: see text] convergence, and quantitative estimates with respect to the [Formula: see text] norm, [Formula: see text]-functionals and [Formula: see text]-modulus of continuity as well. The results are tested on several examples of kernels and possible extensions to higher dimensions are suggested.

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