ON THE EXACT PENALTY OF HIGH ORDER FOR EXTREME PROBLEMS OF DIFFERENTIAL INCLUSIONS

In this paper, using theorems on the continuous dependence of the solution of differential inclusions on the perturbation, we obtain high-order exact penalty theorems for nonconvex extremal problems of differential inclusions in the space of Banach-valued absolutely continuous functions. Using the type of the distance function in the classes of 𝜙 − (𝜙, 𝜙, 𝜙, 𝜙, 𝜙) locally Lipschitz functions, the nonconvex extremal problem for differential inclusions is reduced to a variational problem and the necessary condition for the extremum of a high-order is obtained. The paper also shows that the used functions type of distance function satisfy the 𝜙 − (𝜙, 𝜙, 𝜙, 𝜙, 𝜙) locally Lipschitz conditions.

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VARIATION PROBLEM CONTAINING SECOND DERIVATIVES OF UNKNOWN FUNCTIONS

Chronos: natural and technical sciences ◽

10.52013/2712-9691-34-1-6 ◽

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.

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On Finite Part Integrals and Hadamard-Type Fractional Derivatives

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4037930 ◽

2018 ◽

Vol 13 (9) ◽

Cited By ~ 8

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.

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The spectral theorem for well-bounded operators

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics ◽

10.1017/s1446788700031827 ◽

1993 ◽

Vol 54 (3) ◽

pp. 334-351 ◽

Cited By ~ 1

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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