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Báo cáo hóa học: " TRANSFER POSITIVE HEMICONTINUITY AND ZEROS, COINCIDENCES, AND FIXED POINTS OF MAPS IN TOPOLOGICAL VECTOR SPACES"

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: TRANSFER POSITIVE HEMICONTINUITY AND ZEROS, COINCIDENCES, AND FIXED POINTS OF MAPS IN TOPOLOGICAL VECTOR SPACES | TRANSFER POSITIVE HEMICONTINUITY AND ZEROS COINCIDENCES AND FIXED POINTS OF MAPS IN TOPOLOGICAL VECTOR SPACES K. WLODARCZYK AND D. KLIM Received 9 November 2004 and in revised form 13 December 2004 Let E be a real Hausdorff topological vector space. In the present paper the concepts of the transfer positive hemicontinuity and strictly transfer positive hemicontinuity of set-valued maps in E are introduced condition of strictly transfer positive hemicontinuity is stronger than that of transfer positive hemicontinuity and for maps F C 2E and G C 2E defined on a nonempty compact convex subset C of E we describe how some ideas of K. Fan have been used to prove several new and rather general conditions in which transfer positive hemicontinuity plays an important role that a single-valued map o ucec F c X G c E has a zero and at the same time we give various characterizations of the class of those pairs F G and maps F that possess coincidences and fixed points respectively. Transfer positive hemicontinuity and strictly transfer positive hemicontinuity generalize the famous Fan upper demicontinuity which generalizes upper semicontinuity. Furthermore a new type of continuity defined here essentially generalizes upper hemicontinuity the condition of upper demicontinuity is stronger than the upper hemicontinuity . Comparison of transfer positive hemicontinuity and strictly transfer positive hemicontinuity with upper demicontinuity and upper hemicontinuity and relevant connections of the results presented in this paper with those given in earlier works are also considered. Examples and remarks show a fundamental difference between our results and the well-known ones. 1. Introduction One of the most important tools of investigations in nonlinear and convex analysis is the minimax inequality of Fan 11 Theorem 1 . There are many variations generalizations and applications of this result see e.g. Hu and Papageorgiou 16 17 Ricceri and Simons 19 Yuan 21 22 Zeidler 24 and the .