On generalized weakly directional contractions and approximate fixed point property with applications
Tóm tắt
Từ khóa
Tài liệu tham khảo
Takahashi W: Nonlinear Functional Analysis. Yokohama Publishers, Yokohama, Japan; 2000.
Nadler SB Jr: Multi-valued contraction mappings. Volume 30. Pacific J Math; 1969:475–488.
Mizoguchi N, Takahashi W: Fixed point theorems for multivalued mappings on complete metric spaces. J Math Anal Appl 1989, 141: 177–188. 10.1016/0022-247X(89)90214-X
Daffer PZ, Kaneko H: Fixed points of generalized contractive multi-valued mappings. J Math Anal Appl 1995, 192: 655–666. 10.1006/jmaa.1995.1194
Berinde M, Berinde V: On a general class of multi-valued weakly Picard mappings. J Math Anal Appl 2007, 326: 772–782. 10.1016/j.jmaa.2006.03.016
Hussain N, Cho YJ: Weak contraction, common fixed points and invariant approximations. J Inequal Appl 2009. 2009, Article ID 390634, 10
Hussain N, Amini-Harandi A, Cho YJ: Approximate endpoints for set-valued contractions in metric spaces. Fixed Point Theory Appl 2010., 13: 2010, Article ID 614867,
Kamran T: Multivalued f -weakly Picard mappings. Nonlinear Anal 2007, 67: 2289–2296. 10.1016/j.na.2006.09.010
Huang L-G, Zhang X: Cone metric spaces and fixed point theorems of contractive mappings. J Math Anal Appl 2007, 332: 1468–1476. 10.1016/j.jmaa.2005.03.087
Abbas M, Jungck G: Common fixed point results for noncommuting mappings without continuity in cone metric spaces. J Math Anal Appl 2008, 341: 416–420. 10.1016/j.jmaa.2007.09.070
Rezapour Sh, Hamlbarani R: Some notes on the paper "Cone metric spaces and fixed point theorems of contractive mappings". J Math Anal Appl 2008, 345: 719–724. 10.1016/j.jmaa.2008.04.049
Berinde V, Păcurar M: Fixed points and continuity of almost contractions. Fixed Point Theory 2008, 9: 23–34.
Du W-S: Fixed point theorems for generalized Hausdorff metrics. Int Math Forum 2008, 3: 1011–1022.
Du W-S: Some new results and generalizations in metric fixed point theory. Nonlinear Anal 2010, 73: 1439–1446. 10.1016/j.na.2010.05.007
Du W-S: Coupled fixed point theorems for nonlinear contractions satisfied Mizoguchi-Takahashi's condition in quasiordered metric spaces. Fixed Point Theory and Applications 2010., 9: 2010, Article ID 876372,
Du W-S: Nonlinear Contractive Conditions for Coupled Cone Fixed Point Theorems. Fixed Point Theory and Applications 2010., 16: 2010, Article ID 190606,
Du W-S: New cone fixed point theorems for nonlinear multivalued maps with their applications. Appl Math Lett 2011, 24: 172–178. 10.1016/j.aml.2010.08.040
Du W-S, Zheng S-X: Nonlinear conditions for coincidence point and fixed point theorems. Taiwanese J Math 2012, 16(3):857–868.
Du W-S: On coincidence point and fixed point theorems for nonlinear multivalued maps. Topol Appl 2012, 159: 49–56. 10.1016/j.topol.2011.07.021
Clarke FH: Pointwise contraction criteria for the existence of fixed points. Can Math Bull 1978, 21(1):7–11. 10.4153/CMB-1978-002-8
Sehgal VM, Smithson RE: A fixed point theorem for weak directional contraction multifunction. Math Japon 1980, 25(3):345–348.
Song W: A generalization of Clarke's fixed point theorem. Appl Math J Chin Univ Ser B 1995, 10(4):463–466. 10.1007/BF02662502
Uderzo A: Fixed points for directional multi-valued k (·)-contractions. J Global Optim 2005, 31: 455–469. 10.1007/s10898-004-0571-z
Frigon M: Fixed point results for multivalued maps in metric spaces with generalized inwardness conditions. Fixed Point Theory Appl 2010., 19: 2010, Article ID 183217,
Kada O, Suzuki T, Takahashi W: Nonconvex minimization theorems and fixed point theorems in complete metric spaces. Math Japon 1996, 44: 381–391.
Lin L-J, Du W-S: Ekeland's variational principle, minimax theorems and existence of noncon-vex equilibria in complete metric spaces. J Math Anal Appl 2006, 323: 360–370. 10.1016/j.jmaa.2005.10.005
Lin L-J, Du W-S: Some equivalent formulations of generalized Ekeland's variational principle and their applications. Nonlinear Anal 2007, 67: 187–199. 10.1016/j.na.2006.05.006
Lin L-J, Du W-S: On maximal element theorems, variants of Ekeland's variational principle and their applications. Nonlinear Anal 2008, 68: 1246–1262. 10.1016/j.na.2006.12.018
Du W-S: Critical point theorems for nonlinear dynamical systems and their applications. Fixed Point Theory Appl 2010., 16: 2010, Article ID 246382,
He Z, Du W-S, Lin I-J: The existence of fixed points for new nonlinear multivalued maps and their applications. Fixed Point Theory and Applications 2011 2011, 84.
Ding XP, He YR: Fixed point theorems for metrically weakly inward set-valued mappings. J Appl Anal 1999, 5(2):283–293.
Downing D, Kirk WA: Fixed point theorems for set-valued mappings in metric and Banach spaces. Math Japon 1977, 22: 99–112.
Reich S: A fixed point theorem for locally contractive multivalued functions. Rev Roumaine Math Pures Appl 1972, 17: 569–572.
Reich S: Fixed points of contractive functions. Boll Un Mat Ital 1972, 5(4):26–42.