A fixed point theorem for G-monotone multivalued mapping with application to nonlinear integral equations

Kamran, Tayyab; Vetro, Calogero; Ali, Muhammad Usman; Waheed, Mehwish

doi:10.2298/fil1707045k

Cited by 3 publications

(4 citation statements)

References 15 publications

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“…and transform the integral of A(t). Consequently in this way, repeating the techniques from [21] by analogy it can be shown the following remarkable integral representation of A(t) (see (9)…”

Section: Sufficient Conditions Of Optimality For (P H )mentioning

confidence: 80%

“…In turn by substituting the expression for η * k (t), k = 1, ..., m − 1 into the first equation in (21) we can define the following Euler-Lagrange type adjoint differential inclusion (equation);…”

Section: Applications Of Higher Order Optimization For (P H ) To Calcmentioning

confidence: 99%

“…There is a great number of papers dealing with optimal control theory of ordinary and partial differential inclusions (see [1]- [7], [9], [10]- [12], [17], [18], [21], [22] and their references) and has numerous applications in both science and engineering. The problems accompanied with the higher order ordinary differential inclusions are more complicated due to the higher order derivatives.…”

Section: Introductionmentioning

confidence: 99%

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Optimization of Lagrange problem with higher order differential inclusions and endpoint constraints

Mahmudov

2018

Filomat

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In the paper minimization of a Lagrange type cost functional over the feasible set of solutions of higher order differential inclusions with endpoint constraints is studied. Our aim is to derive sufficient conditions of optimality for m th-order convex and non-convex differential inclusions. The sufficient conditions of optimality containing the Euler-Lagrange and Hamiltonian type inclusions as a result of endpoint constraints are accompanied by so-called ?endpoint? conditions. Here the basic apparatus of locally adjoint mappings is suggested. An application from the calculus of variations is presented and the corresponding Euler-Poisson equation is derived. Moreover, some higher order linear optimal control problems with quadratic cost functional are considered and the corresponding Weierstrass-Pontryagin maximum principle is constructed. Also at the end of the paper some characteristic features of the obtained result are illustrated by example with second order linear differential inclusions.

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Section: Sufficient Conditions Of Optimality For (P H )mentioning

confidence: 80%

Section: Applications Of Higher Order Optimization For (P H ) To Calcmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimization of Lagrange problem with higher order differential inclusions and endpoint constraints

Mahmudov

2018

Filomat

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“…Convex optimization has a wide range of applications in many areas, such as combinatorial optimization and global optimization, where it is used to find bounds on optimal value as well as approximate solutions. However, it is commonly used in the fields of economy and engineering, electronic process automation, automatic control systems and optimum design problems in electrical, chemical, mechanical and aerospace engineering [1], [7], [8], [10], [12], [30]- [35].…”

Section: Introductionmentioning

confidence: 99%

Optimality conditions for higher order polyhedral discrete and differential inclusions

Sağlam

Mahmudov

2020

Filomat

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The problems considered in this paper are described in polyhedral multi-valued mappings for higher order(s-th) discrete (PDSIs) and differential inclusions (PDFIs). The present paper focuses on the necessary and sufficient conditions of optimality for optimization of these problems. By converting the PDSIs problem into a geometric constraint problem, we formulate the necessary and sufficient conditions of optimality for a convex minimization problem with linear inequality constraints. Then, in terms of the Euler-Lagrange type PDSIs and the specially formulated transversality conditions, we are able to obtain conditions of optimality for the PDSIs. In order to obtain the necessary and sufficient conditions of optimality for the discrete-approximation problem PDSIs, we reduce this problem to the form of a problem with higher order discrete inclusions. Finally, by formally passing to the limit, we establish the sufficient conditions of optimality for the problem with higher order PDFIs. Numerical approach is developed to solve a polyhedral problem with second order polyhedral discrete inclusions.

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Best proximity point results for Prešić type nonself operators in $ b $-metric spaces

Batul

Sagheer

Aydi

et al. 2022

MATH

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A fixed point theorem for G-monotone multivalued mapping with application to nonlinear integral equations

Cited by 3 publications

References 15 publications

Optimization of Lagrange problem with higher order differential inclusions and endpoint constraints

Optimization of Lagrange problem with higher order differential inclusions and endpoint constraints

Optimality conditions for higher order polyhedral discrete and differential inclusions

Best proximity point results for Prešić type nonself operators in $ b $-metric spaces

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