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Các điểm cố định trong không gian metric có thứ tự với các ứng dụng trong lý thuyết đồng homotopy
Tóm tắt
Trong bài báo này, chúng tôi chứng minh các định lý điểm cố định cho các ánh xạ thỏa mãn một quan hệ ngầm trong không gian metric có thứ tự. Như một ứng dụng, chúng tôi đạt được một kết quả đồng homotopy. Kết quả của chúng tôi chỉnh sửa/mở rộng một số kết quả điểm cố định đã có trong tài liệu nghiên cứu.
Từ khóa
#điểm cố định #không gian metric có thứ tự #lý thuyết đồng homotopy #ánh xạ #định lý.Tài liệu tham khảo
Agarwal, R.P., El-Gebeily, M.A., O’Regan, D.: Generalized contractions in partially ordered metric spaces. Appl. Anal. 87(1), 109–116 (2008)
Altun, I., Erduran, A.: A Suzuki type fixed point theorem. Int. J. Math. Math. Sci 2011, 9 (2011)
Altun, I., Hancer, H.A., Turkoglu, D.: A fixed point theorem for multi maps satisfying an implicit relation on metrically convex metric spaces. Math. Commun. 11, 17–23 (2006)
Altun, I., Simsek, H.: Some fixed point theorems on ordered metric spaces and applications. Fixed Point Theory Appl. 2010, 17 (2010)
Altun, I., Sola, F., Simsek, H.: Generalized contractions on partial metric spaces. Topol. Its Appl. 157, 2778–2785 (2010)
Altun, I., Turkoglu, D.: Some fixed point theorems for weakly compatible mappings satisfying an implicit relation. Taiwan. J. Math. 13, 1291–1304 (2009)
Banach, S.: Sur les operations dans les ensembles abstraits et leur application aux équation intégrales. Fund. Math. 3, 133–181 (1922)
Beg, I., Butt, A.R.: Fixed point for set valued mappings satisfying an implicit relation in partially ordered metric spaces. Nonlinear Anal. 71, 3699–3704 (2009)
Beg, I., Butt, A.R.: Fixed points for weakly compatible mappings satisfying an implicit relation in partially ordered metric spaces. Carpath. J. Math. 25, 1–12 (2009)
Berinde, V., Vetro, F.: Common fixed points of mappings satisfying implicit contractive conditions. Fixed Point Theory Appl. 2012, 8 (2012)
Berinde, V.: Stability of Picard iteration for contractive mappings satisfying an implicit relation. Carpath. J. Math. 27, 13–23 (2011)
Ćirić, L.J., Cakid, N., Rajovic, M., Uma, J.S.: Monotone generalized nonlinear contractions in partially ordered metric spaces Fixed Point Theory and Appl. (2008)
Ćirić, Lj: A generalization of Banach’s contraction principle. Proc. Am. Math. Soc. 45, 267–273 (1974)
Chatterjea, S.K.: Fixed point theorem. C. R. Acad. Bulg. Sci. 25, 727–730 (1972)
Bhaskar, T.Gnana, Lakshmikantham, V.: Fixed point theorems in partially ordered metric spaces and applications. Nonlinear Anal. 65, 1379–1393 (2006)
Harjani, J., Sadarangani, K.: Fixed point theorems for weakly contractive mappings in partially ordered sets. Nonlinear Anal. 71, 3403–3410 (2009)
Goebel, K., Reich, S.: Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings. Marcel Dekker, New York (1984)
Kirk, W.A., Goebel, K.: Topics in Metric Fixed Point Theory. Cambridge University Press, Cambridge (1990)
Lakshmikantham, V., Ćirić, Lj: Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces. Nonlinear Anal. 70, 4341–4349 (2009)
Nieto, J.J., Rodríguez-López, R.: Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations. Order. 22, 223–239 (2005)
Nieto, J.J., Rodríguez-López, R.: Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations. Acta Math. Sin. 23(12), 2205–2212 (2007)
Nieto, J.J., Pouso, R.L., Rodríguez-López, R.: Fixed point theorems in ordered abstract spaces. Proc. Am. Math. Soc. 8, 2505–2517 (2007)
O’Regan, D., Petrusel, A.: Fixed point theorems for generalized contractions in ordered metric spaces. J. Math. Anal. Appl. 341, 1241–1252 (2008)
Popa, V.: Fixed point theorems for implicit contractive mappings. Stud. Cerc. Şt. Ser. Mat. Univ. Bacău 7, 127–134 (1997)
Popescu, O.: A partial generalization of a Ćirić theorem. J. Nonlinear Sci. Appl. 6, 152–161 (2015)
Ran, A.C.M., Reurings, M.C.B.: A fixed point theorem in partially ordered sets and some applications to matrix equations. Proc. Am. Math. Soc. 132, 1435–1443 (2004)
Sedghi, S., Altun, I., Shobe, N.: A fixed point theorem for multi maps satisfying an implicit relation on metric spaces. Appl. Anal. Discret. Math. 2, 189–196 (2008)