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Variational Inclusions Involving Difference of Operators

Thesis Info

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Author

Kamal, Rabia

Program

PhD

Institute

COMSATS University Islamabad

City

Islamabad

Province

Islamabad.

Country

Pakistan

Thesis Completing Year

2017

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/13622/1/Rabia_kamal_Maths_2017_CIIT_HSR_14.04.2017.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727657740

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A new class of general variational inclusions involving difference of operators has been investigated. Using resolvent operator and resolvent equations technique, it is shown that general variational inclusions and fixed point problems are equivalent. Using this equivalent formulations, we prove the existence of a solution of general variational inclusion. Iterative schemes and its convergence is also discussed. We study some dynamical systems associated with variational inclusion. The dynamical system is used to discuss the existence of the variational inclusion using Lipschitz continuity only. Some Merit functions are constructed for the variational inclusions. Using these merit functions, some error estimates are obtained under suitable assumptions. Sensitivity analysis is analyzed using the resolvent equations. Several classes of variational inclusion and optimization problem are discussed which can be obtained as special cases from our results.
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