DERIVATIVES OF VARIATION FUNCTIONS AND OF MUTUTLLY SINGULAR AND RELATIVELY ABSOLUTELY CONTINUOUS FUNCTIONS

1984 ◽  
Vol 10 (1) ◽  
pp. 54 ◽  
Author(s):  
Garg
Keyword(s):  
Continuous Functions ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous ◽  
Derivatives Of

scholarly journals Approximation by generalized positive linear Kantorovich operators

Filomat ◽  
2017 ◽  
Vol 31 (14) ◽  
pp. 4353-4368 ◽  
Author(s):  
Minakshi Dhamija ◽  
Naokant Deo
Keyword(s):  
Rate Of Convergence ◽  
Approximation Theorem ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Continuous Functions ◽  
Approximation Properties ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous ◽  
Derivatives Of ◽  
Kantorovich Operators

In the present article, we introduce generalized positive linear-Kantorovich operators depending on P?lya-Eggenberger distribution (PED) as well as inverse P?lya-Eggenberger distribution (IPED) and for these operators, we study some approximation properties like local approximation theorem, weighted approximation and estimation of rate of convergence for absolutely continuous functions having derivatives of bounded variation.

scholarly journals VARIATION PROBLEM CONTAINING SECOND DERIVATIVES OF UNKNOWN FUNCTIONS

2021 ◽  
Vol 6 (1(34)) ◽  
pp. 30-42
Author(s):  
Misraddin Allahverdi oglu Sadigov
Keyword(s):  
Variational Problem ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Necessary Condition ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous ◽  
Variation Problem ◽  
Second Derivatives ◽  
Necessary And Sufficient ◽  
Derivatives Of

The property subdifferential of an integral and terminal functional in a space of the type of absolutely continuous functions is studied. Necessary and sufficient conditions for an extremum for a variational problem containing the second derivatives of unknown functions are obtained. With the help of the subdifferential introduced by the author, a nonconvex generalized variational problem containing the second derivatives of unknown functions is considered, and the necessary condition for an extremum is obtained.

scholarly journals Rate of convergence of beta operators of second kind for functions with derivatives of bounded variation

2005 ◽  
Vol 2005 (23) ◽  
pp. 3827-3833 ◽  
Author(s):  
Vijay Gupta ◽  
Ulrich Abel ◽  
Mircea Ivan
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
Continuous Functions ◽  
Function Of Bounded Variation ◽  
Approximation Properties ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous ◽  
Derivatives Of

We study the approximation properties of beta operators of second kind. We obtain the rate of convergence of these operators for absolutely continuous functions having a derivative equivalent to a function of bounded variation.

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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