Note on essential fixed points of approximable multivalued mappings

被引：0

作者：

Andres J. ^{[1
]}

Górniewicz L. ^{[2
]}

机构：

[1] Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacký University, 17. listopadu 12, Olomouc

[2] Institute of Mathematics, University of Kazimierz Wielki, Weyssenhoffa 11, Bydgoszcz

来源：

Fixed Point Theory and Applications | / 2016卷 / 1期

关键词：

absolute neighborhood retracts; approximable multivalued mappings; discretely essential periodic solutions; dissipative differential inclusions; essential fixed points; fixed point index; J-maps; Lefschetz number; Poincaré translation operators;

D O I：

10.1186/s13663-016-0568-6

中图分类号：

学科分类号：

摘要：

A new definition of essential fixed points is introduced for a large class of multivalued maps. Two abstract existence theorems are presented for approximable maps on compact ANR-spaces in terms of a nontrivial fixed point index, or a nontrivial Lefschetz number and a zero topological dimension of the fixed point set. The second one is applied to the periodic dissipative Marchaud differential inclusions for obtaining the existence of a discretely essential subharmonic solution. Three simple illustrative examples are supplied. © 2016, Andres and Górniewicz.

引用

共 19 条

[1]

Andres J., Gorniewicz L., On essential fixed points of compact mappings on arbitrary absolute neighborhood retracts and their application to multivalued fractals, Int. J. Bifurc. Chaos, 26, 3, (2016)

[2]

Andres J., Gorniewicz L., Recent results on the topological fixed point theory of multivalued mappings: a survey, Fixed Point Theory Appl., 2015, (2015)

[3]

Fort M.K., Essential and non essential fixed points, Am. J. Math., 72, pp. 315-322, (1950)

[4]

O'Neil B., Essential sets and fixed points, Am. J. Math., 75, pp. 497-509, (1953)

[5]

Del Prete I., Naimpally S., di Iorio M., Essential fixed points of functions and multifunctions, Real Anal. Exch., 25, 1, pp. 369-382, (1999)

[6]

Jiang J., Essential fixed points of the multivalued mappings, Sci. China Math., 11, 3, pp. 293-298, (1962)

[7]

Andres J., Gorniewicz L., Topological Fixed Point Principles for Boundary Value Problems, (2003)

[8]

Gorniewicz L., Topological Fixed Point Theory of Multivalued Mappings, (2006)

[9]

Ben-El-Mechaiekh H., Spaces and maps approximation and fixed points, J. Comput. Appl. Math., 113, 1-2, pp. 283-308, (2000)

[10]

Gorniewicz L., Granas A., Kryszewski W., On the homotopy method in the fixed point index theory of multivalued mappings of compact absolute neighborhood retracts, J. Math. Anal. Appl., 161, 2, pp. 457-473, (1991)

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