scholarly journals Approximation by sampling-type nonlinear discrete operators in φ-variation

Filomat ◽  
2021 ◽  
Vol 35 (8) ◽  
pp. 2731-2746
Author(s):  
İsmail Aslan
Keyword(s):  
Close Relationships ◽  
Nonlinear Approximation ◽  
Continuous Functions ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous ◽  
Lipschitz Classes ◽  
Generalized Sampling ◽  
Convergence In Variation ◽  
Sampling Series ◽  
Discrete Operators

In the present paper, our purpose is to obtain a nonlinear approximation by using convergence in ?-variation. Angeloni and Vinti prove some approximation results considering linear sampling-type discrete operators. These types of operators have close relationships with generalized sampling series. By improving Angeloni and Vinti?s one, we aim to get a nonlinear approximation which is also generalized by means of summability process. We also evaluate the rate of approximation under appropriate Lipschitz classes of ?-absolutely continuous functions. Finally, we give some examples of kernels, which fulfill our kernel assumptions.

scholarly journals Approximation by pseudo-linear discrete operators

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
İsmail Aslan ◽  
Türkan Yeliz Gökçer
Keyword(s):  
Error Estimation ◽  
Modulus Of Continuity ◽  
Continuous Functions ◽  
Discrete Operator ◽  
Generalized Sampling ◽  
Sampling Series ◽  
Discrete Operators ◽  
Generator Function ◽  
Uniformly Continuous

<p style='text-indent:20px;'>In this note, we construct a pseudo-linear kind discrete operator based on the continuous and nondecreasing generator function. Then, we obtain an approximation to uniformly continuous functions through this new operator. Furthermore, we calculate the error estimation of this approach with a modulus of continuity based on a generator function. The obtained results are supported by visualizing with an explicit example. Finally, we investigate the relation between discrete operators and generalized sampling series.</p>

On Finite Part Integrals and Hadamard-Type Fractional Derivatives

2018 ◽  
Vol 13 (9) ◽  
Author(s):  
Li Ma ◽  
Changpin Li
Keyword(s):  
Fractional Derivative ◽  
Singular Integral ◽  
Fractional Derivatives ◽  
Continuous Functions ◽  
Finite Part ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous ◽  
Fundamental Properties ◽  
Logarithmic Series ◽  
The Right

This paper is devoted to investigating the relation between Hadamard-type fractional derivatives and finite part integrals in Hadamard sense; that is to say, the Hadamard-type fractional derivative of a given function can be expressed by the finite part integral of a strongly singular integral, which actually does not exist. Besides, our results also cover some fundamental properties on absolutely continuous functions, and the logarithmic series expansion formulas at the right end point of interval for functions in certain absolutely continuous spaces.

scholarly journals The spectral theorem for well-bounded operators

1993 ◽  
Vol 54 (3) ◽  
pp. 334-351 ◽  
Author(s):  
Ian Doust ◽  
Qiu Bozhou
Keyword(s):  
Functional Calculus ◽  
Continuous Functions ◽  
Weak Compactness ◽  
Compact Interval ◽  
Spectral Theorem ◽  
Type B ◽  
Bounded Operators ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous

AbstractWell-bounded operators are those which possess a bounded functional calculus for the absolutely continuous functions on some compact interval. Depending on the weak compactness of this functional calculus, one obtains one of two types of spectral theorem for these operators. A method is given which enables one to obtain both spectral theorems by simply changing the topology used. Even for the case of well-bounded operators of type (B), the proof given is more elementary than that previously in the literature.

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