×

Fixed points of generalized \(\alpha \)-\(\psi \)-contractions. (English) Zbl 1334.54059

In this paper, the authors introduce the class of \(\alpha-\psi\)-contractive maps and multifunctions defined on a complete metric space \(X\); here, \(\alpha:X\times X\to [-0,\infty)\) and \(\psi:[0,\infty)\to [0,\infty)\) are given functions satisfying some assumptions. Some results concerning fixed points of such maps are proved. No examples of applications are presented.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
54C60 Set-valued maps in general topology
54E50 Complete metric spaces
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Kilm, D., Wardowski, D.: Dynamic processes and fixed points of set-valued nonlinear contractions in cone metric spaces. Nonlinear Anal. 71, 5170-5175 (2009) · Zbl 1203.54042 · doi:10.1016/j.na.2009.04.001
[2] Balaj, M.: A unified generalization of two Halpern’s fixed point theorems and applications. Num. Funct. Anal. Optim. 23(1-2), 105-111 (2002) · Zbl 1020.47043 · doi:10.1081/NFA-120003673
[3] Halpern, B.: Fixed point theorems for set-valued maps in infinite dimensional spaces. Math. Ann. 189, 87-98 (1970) · Zbl 0191.14701
[4] Rezapour, Sh, Amiri, P.: Fixed point of multivalued operators on ordered generalized metric spaces. Fixed Point Theory 13(1), 173-178 (2012) · Zbl 1329.54053
[5] Rezapour, Sh, Amiri, P.: Some fixed point results for multivalued operators in generalized metric spaces. Comput. Math. Appl. 61, 2661-2666 (2011) · Zbl 1221.54071 · doi:10.1016/j.camwa.2011.03.014
[6] Rezapour, Sh, Khandani, H., Vaezpour, S.M.: Efficacy of cones on topological vector spaces and application to common fixed points of multifunctions. Rend. Circ. Mat. Palermo 59, 185-197 (2010) · Zbl 1198.54087 · doi:10.1007/s12215-010-0014-2
[7] Rezapour, Sh, Haghi, R.H.: Fixed point of multifunctions on cone metric spaces. Num. Func. Anal. Optim. 30(7-8), 825-832 (2009) · Zbl 1171.54033 · doi:10.1080/01630560903123346
[8] Rezapour, Sh, Haghi, R.H.: Two results about fixed points of multifunctions. Bull. Iranian Math. Soc. 36(2), 279-287 (2010) · Zbl 1231.47058
[9] Aleomraninejad, S.M.A., Rezapour, Sh, Shahzad, N.: Fixed points of hemi-convex multifunctions. Topol. Methods Nonlinear Anal. 37(2), 383-389 (2011) · Zbl 1462.47031
[10] Kikkawa, M., Suzuki, T.: Three fixed point theorems for generalized contractions with constants in complete metric spaces. Nonlinear Anal. 69, 2942-2949 (2008) · Zbl 1152.54358 · doi:10.1016/j.na.2007.08.064
[11] Suzuki, T.: A generalized Banach contraction principle that characterizes metric completeness. Proc. Amer. Math. Soc. 136, 1861-1869 (2008) · Zbl 1145.54026 · doi:10.1090/S0002-9939-07-09055-7
[12] Samet, B., Vetro, C., Vetro, P.: Fixed point theorems for \[\alpha -\psi \]-contractive type mappings. Nonlinear Anal. 75, 2154-2165 (2012) · Zbl 1242.54027
[13] Rezapour, Sh, Haghi, R.H., Rhoades, B.E.: Some results about T-stability and almost T-stability. Fixed Point Theory 12(1), 179-186 (2011) · Zbl 1281.47052
[14] B. Djafari Rouhani, S. Moradi, Common fixed point of multivalued generalized \[\varphi \]-weak contractive mappings, Fixed Point Theory Appl. Article ID 708984, 13 pages (2010) · Zbl 1202.54041
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.