Brondsted order in a metric space and generalizations of Caristi theorem

Moscow University Mathematics Bulletin - Tập 72 Số 5 - Trang 199-202 - 2017
Т. Н. Фоменко1
1Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia

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Tài liệu tham khảo

Handbook of Metric Fixed Point Theory, Ed. by W.A. Kirk and B. Sims (Springer Science & Business Media, N.Y., 2001).

S. Abian and A. B. Brown, “A Theorem on Partially Ordered Sets, with Applications to Fixed Point Theorems,” Can. J. Math. 13, 78 (1961).

R. E. Smithson, “Fixed Points of Order Preserving Multifunctions,” Proc. Amer. Math. Soc. 2, 304 (1971).

E. Zermelo, “Beweis, das jede Menge wohlgeordnet werden kann,” Math. Ann. 59, 514 (1904).

E. Zermelo, “Neuer Beweis f¨ur die Miiglichkeit einer Wohlordnung,” Math. Ann. 65, 107 (1908).

S. B. Nadler Jr., “Multi-Valued Contraction Mappings,” Pacif. J. Math. 30, 475 (1969).

I. Ekeland, “On the Variational Principle,” J. Math. Anal. Appl. 47, 324 (1974).

R. De Marr, “Partially Ordered Spaces and Metric Spaces,” Amer. Math. Month. 72 (6), 628 (1965).

E. Bishop and R. R. Phelps, “The Support Functionals of a Convex Set”, in Convexity, ed. by V. L. Klee, Proc. Symp. Pure Math., VII (Amer. Math. Soc, Providence, RI, 1963), pp. 27–35.

J. Jachymski, “Some Consequences of Fundamental Ordering Principles in Metric Fixed Point Theory,” Ann. Univ. M. Curie-Sklodowska. Sec. A 51, 123 (1997).

A. Brøndsted, “On a Lemma of Bishop and Phelps,” Pacif. J. Math. 55, 335 (1974).

J. Caristi, “Fixed Point Theorems for Mappings Satisfying Inwardness Conditions,” Trans. Amer. Math. Soc. 215, 241 (1976).

D. A. Podoprikhin and T. N. Fomenko, “On Coincidences of Families of Mappings on Ordered Sets,” Doklady Russ. Akad. Nauk, Matem. 471 (1), 16 (2016) [Doklady Math. 94 (3), 620 (2016)].

T. N. Fomenko and D. A. Podoprikhin, “Common Fixed Points and Coincidences of Mapping Families on Partially Ordered Sets,” Topol. and Its Appl. 221, 275 (2017).

T. N. Fomenko and D. A. Podoprikhin, “Fixed Points and Coincidences of Mappings of Partially Ordered Sets,” J. Fixed Point Theory and its Appl. 18, 823 (2016).