×

zbMATH — the first resource for mathematics

Approximate endpoints for set-valued contractions in metric spaces. (English) Zbl 1202.54033
In the present paper, the authors establish some existence results concerning approximate fixed points, endpoints and approximate endpoints of multivalued contractions. Qualitative estimates of the sets of approximate fixed points and approximate endpoints for set-valued almost I-contractions are also developed.

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] Barroso, CS, The approximate fixed point property in Hausdorff topological vector spaces and applications, Discrete and Continuous Dynamical Systems, 25, 467-479, (2009) · Zbl 1178.47034
[2] Khamsi, MA, On asymptotically nonexpansive mappings in hyperconvex metric spaces, Proceedings of the American Mathematical Society, 132, 365-373, (2004) · Zbl 1043.47040
[3] Lin, PK; Sternfeld, Y, Convex sets with the Lipschitz fixed point property are compact, Proceedings of the American Mathematical Society, 93, 633-639, (1985) · Zbl 0566.47039
[4] Amini-Harandi, A, Endpoints of set-valued contractions in metric spaces, Nonlinear Analysis: Theory, Methods & Applications, 72, 132-134, (2010) · Zbl 1226.54042
[5] Berinde, M, Approximate fixed point theorems, Studia. Universitatis Babeş-Bolyai. Mathematica, 51, 11-25, (2006) · Zbl 1164.54028
[6] Berinde, M; Berinde, V, On a general class of multi-valued weakly Picard mappings, Journal of Mathematical Analysis and Applications, 326, 772-782, (2007) · Zbl 1117.47039
[7] Ćirić, L, Multi-valued nonlinear contraction mappings, Nonlinear Analysis: Theory, Methods & Applications, 71, 2716-2723, (2009) · Zbl 1179.54053
[8] Hussain, N; Cho, YJ, Weak contractions, common fixed points, and invariant approximations, No. 2009, 10, (2009) · Zbl 1183.47049
[9] Klim, D; Wardowski, D, Fixed point theorems for set-valued contractions in complete metric spaces, Journal of Mathematical Analysis and Applications, 334, 132-139, (2007) · Zbl 1133.54025
[10] Păcurar, M; Păcurar, RV, Approximate fixed point theorems for weak contractions on metric spaces, Carpathian Journal of Mathematics, 23, 149-155, (2007) · Zbl 1174.54029
[11] Hussain, N, Common fixed points in best approximation for Banach operator pairs with ćirić type [inlineequation not available: see fulltext.]-contractions, Journal of Mathematical Analysis and Applications, 338, 1351-1363, (2008) · Zbl 1134.47039
[12] Feng, Y; Liu, S, Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings, Journal of Mathematical Analysis and Applications, 317, 103-112, (2006) · Zbl 1094.47049
[13] Aubin, J-P; Siegel, J, Fixed points and stationary points of dissipative multivalued maps, Proceedings of the American Mathematical Society, 78, 391-398, (1980) · Zbl 0446.47049
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.