TAILIEUCHUNG - Báo cáo hóa học: " Research Article The Theory of Reich’s Fixed Point Theorem for Multivalued Operators"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article The Theory of Reich’s Fixed Point Theorem for Multivalued Operators | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 178421 10 pages doi 2010 178421 Research Article The Theory of Reich s Fixed Point Theorem for Multivalued Operators Tania Lazar 1 Ghiocel Mot 2 Gabriela Petrusel 3 and Silviu Szentesi4 1 Commercial Academy ofSatu Mare Mihai Eminescu Street No. 5 Satu Mare Romania 2 Aurel Vlaicu University of Arad Elena Dragoi Street No. 2 310330 Arad Romania 3 Department of Business Babeậ-Bolyai University Cluj-Napoca Horea Street No. 7 400174 Cluj-Napoca Romania 4 Aurel Vlaicu University of Arad Revoulịiei Bd. No. 77 310130 Arad Romania Correspondence should be addressed to Ghiocel Mot Received 12 April 2010 Revised 12 July 2010 Accepted 18 July 2010 Academic Editor S. Reich Copyright 2010 Tania Lazar et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. The purpose of this paper is to present a theory of Reich s fixed point theorem for multivalued operators in terms of fixed points strict fixed points multivalued weakly Picard operators multivalued Picard operators data dependence of the fixed point set sequence of multivalued operators and fixed points Ulam-Hyers stability of a multivalued fixed point equation well-posedness of the fixed point problem and the generated fractal operator. 1. Introduction Let X d be a metric space and consider the following family of subsets Pcl X Y c X Y is nonempty and closed . We also consider the following generalized functionals D P X X P X - R D A B inf d a b a e A b e B D is called the gap functional between A and B. In particular if x0 e X then D x0 B D x0 B p P X X P X - R -W. p A B sup D a B a e A p is called the generalized excess functional H P X X P X - R -W. H A B max p A B p B A H is the generalized Pompeiu-Hausdorff functional. 2 Fixed Point

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