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Báo cáo hóa học: " Solving systems of nonlinear matrix equations involving Lipshitzian mappings"

Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Solving systems of nonlinear matrix equations involving Lipshitzian mappings | Berzig and Samet Fixed Point Theory and Applications 2011 2011 89 http www.fixedpointtheoryandapplications.eom content 2011 1 89 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access Solving systems of nonlinear matrix equations involving Lipshitzian mappings Maher Berzig and Bessem Samet Correspondence maher. berzig@gmail.com Université de Tunis Ecole Supérieure des Sciences et Techniques de Tunis 5 Avenue Taha Hussein-Tunis B.P. 56 1008 Bab Menara Tunisia Springer Abstract In this study both theoretical results and numerical methods are derived for solving different classes of systems of nonlinear matrix equations involving Lipshitzian mappings. 2000 Mathematics Subject Classifications 15A24 65H05. Keywords nonlinear matrix equations Lipshitzian mappings Banach contraction principle iterative method fixed point Thompson metric 1 Introduction Fixed point theory is a very attractive subject which has recently drawn much attention from the communities of physics engineering mathematics etc. The Banach contraction principle 1 is one of the most important theorems in fixed point theory. It has applications in many diverse areas. Definition 1.1 Let M be a nonempty set and f M M be a given mapping. We say that x e M is a fixed point offif fx x . Theorem 1.1 Banach contraction principle 1 . Let M d be a complete metric space and f M M be a contractive mapping i.e. there exists l e 0 1 such that for all x y e M d fx fy L d x y . 1 Then the mapping f has a unique fixed point x e M. Moreover for every x0 e M the sequence xk defined by xk 1 fxkfor all k 0 1 2 . converges to x and the error estimate is given by L d xk x d x0 x1 for all k 0 1 2 . 1 - Ằ Many generalizations of Banach contraction principle exists in the literature. For more details we refer the reader to 2-4 . To apply the Banach fixed point theorem the choice of the metric plays a crucial role. In this study we use the Thompson metric introduced by Thompson 5 for the study of solutions