×

zbMATH — the first resource for mathematics

Coincidence and fixed point theorems for nonlinear hybrid generalized contractions. (English) Zbl 0949.54057
Summary: We first prove some coincidence and fixed point theorems for nonlinear hybrid generalized contractions on metric spaces. Secondly, using the concept of an asymptotically regular sequence, we give some fixed point theorems for Kannan type multivalued mappings on metric spaces. Our main results improve and extend several known results proved by other authors.

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] I. Beg and A. Azam: Fixed point theorems for Kannan mappings. Indian J. Pure and Appl. Math. 17(11) (1986), 1270-1275. · Zbl 0607.54034
[2] I. Beg and A. Azam: Fixed points of asymptotically regular multivalued mappings. J. Austral. Math. Soc. (Series A) 53 (1992), 313-326. · Zbl 0765.54036
[3] K. M. Das and K. V. Naik: Common fixed point theorems for commuting maps on a metric space. Proc. Amer. Math. Soc. 77 (1979), 369-373. · Zbl 0418.54025
[4] B. Fisher: Common fixed points of four mappings. Bull. Inst. Math. Acad. Sinica 11 (1983), 103-113. · Zbl 0515.54029
[5] G.Jungck: Commuting mappings and fixed points. Amer. Math. Monthly 83 (1976), 261-163. · Zbl 0321.54025
[6] G.Jungck: Compatible mappings and common fixed points. Internat. J. Math. & Math. Sci. 9 (1986), 771-779. · Zbl 0613.54029
[7] G.Jungck: Common fixed points for commuting and compatible maps on compacta. Proc. Amer. Math. Soc. 103 (1988), 997-983. · Zbl 0661.54043
[8] H. Kaneko: Single-valued and multi-valued f-contractions. Boll. Un. Mat. Ital. 4-A (1985), 29-33. · Zbl 0568.54031
[9] H. Kaneko: A common fixed point of weakly commuting multi-valued mappings. Math. Japonica 33(5) (1988), 741-744. · Zbl 0664.54031
[10] H. Kaneko and S. Sessa: Fixed point theorem for compatible multi-valued and single-valued mappings. Internat. J. Math. & Math. Sci. 12 (1989), 257-262. · Zbl 0671.54023
[11] R. Kannan: Some results on fixed points. Bull. Calcutta. Math. Soc. 60 (1968), 71-76. · Zbl 0209.27104
[12] R. Kannan: Fixed point theorem in reflexive Banach spaces. Proc. Amer. Math. Soc. 38 (1973), 111-118. · Zbl 0265.47038
[13] T. Kubiak: Fixed point theorems for contractive type multi-valued mappings. Math. Japonica 30 (1985), 89-101. · Zbl 0567.54030
[14] H. K. Pathak: On a fixed point theorem of Jungck. to appear in Proceedings of the First World Congress of Nonlinear Analyst, 1992. · Zbl 0841.54033
[15] H. K. Pathak: On common fixed points of weak compatible mappings in metric and Banach spaces. to appear in Nonlinear Functional Analysis and its Applications, special volume (Ed. T. M. Rassias) (1993).
[16] H. K. Pathak: Fixed point theorem for weak compatible multi-valued and single-valued mappings. Acta. Math. Hungar. 67(1-2) (1995), 69-78. · Zbl 0821.54027
[17] H. K. Pathak and V. Popa: On common fixed points of weak compatible mappings in metric spaces. Studii Si Ćercetǎri Stiintifice, Seria: Mathematicǎ 3 (1994), 89-100.
[18] H. K. Pathak and V. Popa: Common fixed points of weak compatible mappings. Studia Univ. Babes-Bolyai Mathematica 34(1) (1994), 65-78. · Zbl 0868.54037
[19] S. Nadler: Multi-valued contraction mappings. Pacific J. Math. 20 (1969), 475-488. · Zbl 0187.45002
[20] B. E. Rhoades, S. Sessa, M. S. Khan and M. Swaleh: On fixed points of asymptotically regular mappings. J. Austral. Math. Soc. (Series A) 43 (1987), 328-346. · Zbl 0659.54042
[21] S. Sessa: On a weak commutativity condition of mappings in fixed point considerations. Publ. Inst. Math. (Beograd) 32(46) (1982), 146-153. · Zbl 0523.54030
[22] C. Shiau, K. K. Tan and C. S. Wong: A class of quasi-nonexpansive multi-valued maps. Canad. Math. Bull. 18 (1975), 707-714. · Zbl 0343.47045
[23] S. L. Singh and S. P. Singh: A fixed point theorem. Indian J. Pure and Appl. Math. 11 (1980), 1584-1586. · Zbl 0461.54034
[24] S. L. Singh, K. S. Ha and Y. J. Cho: Coincidence and fixed points of nonlinear hybrid contractions. Internat. J. Math. & Math. Sci. 12(2) (1989), 247-256. · Zbl 0669.54024
[25] R. E. Smithson: Fixed points for contractive multi-functions. Proc. Amer. Math. Soc. 27 (1971), 192-194. · Zbl 0213.24501
[26] C. S. Wong: On Kannan maps. Proc. Amer. Math. Soc. 47 (1975), 105-111. · Zbl 0265.47039
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.