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Title: Solvability of some classes of nonlinear variational inequalities
Researcher: Mohammad Shahzad
Guide(s): Kaleem Raza Kazmi
Keywords: nonlinear variational inequalities
Upload Date: 19-Sep-2013
University: Aligarh Muslim University
Completed Date: 2012
Abstract: The present thesis entitled Solvability of some classes of nonlinear variational inequalities is an outcome of the studies made by the author at Aligarh Muslim University, Aligarh, India. The main objective of this thesis is to study the existence of solutions and to discuss the convergence analysis of iterative algorithms for some new classes of variational inequalities, system of variational inequalities and variational inclusions. This work generalizes, improves and unifies the concepts, techniques and results for the various classes of variational inequalities and variational inclusions given in the recent literature. The thesis consists of six chapters. In Chapter 1, we review the notations, definitions and results which are used in the presentation of the work of the subsequent chapters. Further, we give brief introduction of some classes of variational inequalities, variational inclusions, system of variational inequalities and system of variational inclusions. In Chapter 2, we give the concepts of partially relaxed strongly mixed monotone and regularized partially relaxed strongly _-pseudomonotone mappings, which are extensions of the concepts given by Xia and Ding [Xia, F.Q. and Ding, X. P., Predictor-corrector algorithms for solving generalized mixed quasi equilibrium problem, Appl. Math. Comput., 188 (2007), 173-179], Noor [Noor, M.A., Regularized mixed quasi equilibrium problems, J. Appl. Math. Comput., 23 (2007), 183-191] and Kazmi et al. [Kazmi, K.R., Khaliq, A. and Raouf, A., Iterative approximation of generalized mixed set-valued variational inequality problem, Math. Inequal. Appl., 10(3) (2007), 677-691]. Further, we use the auxiliary principle technique to suggest a two step iterative algorithm for approximating the solution of regularized (nonconvex) generalized mixed variational inequality problem. We prove that the convergence of the iterative algorithm requires only the continuity, partially relaxed strongly mixed monotonicity and partially relaxed strongly pseudomonotonicity.
Pagination: 109p.
Appears in Departments:Department of Mathematics

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04_dedications.pdf9.74 kBAdobe PDFView/Open
05_abstract.pdf24.34 kBAdobe PDFView/Open
06_chapter-1.pdf120.7 kBAdobe PDFView/Open
07_chapter-2.pdf67.43 kBAdobe PDFView/Open
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09_chapter-4.pdf76.31 kBAdobe PDFView/Open
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11_chapter-6.pdf105.28 kBAdobe PDFView/Open
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