×

Rhoades-type fixed-point theorems for a pair of nonself mappings. (English) Zbl 1065.47059

Using suitable conditions of contractivity and weak commutativity, some common fixed point theorems for a pair of non-self mappings on closed subsets of Banach spaces are proved which generalize results due to Rhoades and Assad. Some examples and applications are also given.

MSC:

47H10 Fixed-point theorems
54H25 Fixed-point and coincidence theorems (topological aspects)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Assad, N. A.; Kirk, W. A., Fixed point theorems for set-valued mappings of contractive type, Pacific J. Math., 43, 3, 553-562 (1972) · Zbl 0239.54032
[2] Assad, N. A., Fixed point theorems for set-valued transformations on compact sets, Bull. Un. Mat. Ital., 4, 7, 1-7 (1973) · Zbl 0265.54046
[3] Hadzic, O.; Gajic, Lj., Coincidence points for set-valued mappings in convex metric spaces, Univ. U. Novom. Sadu. Zb. Rad. Prirod. Mat. Fak. Ser. Mat., 16, 1, 13-25 (1986) · Zbl 0639.54037
[4] Hadzic, O., On coincidence points in convex metric spaces, Univ. U. Novom. Sadu. Zb. Rad. Prirod. Mat. Fak. Ser. Mat., 19, 2, 233-240 (1986) · Zbl 0718.54048
[5] Rhoades, B. E., A fixed point theorem for non-self mappings, Math. Japon., 23, 4, 457-459 (1978) · Zbl 0396.47038
[6] Rhoades, B. E., A fixed point theorem for non-self set-valued mappings, Internat. J. Math. & Math. Sci., 20, 1, 9-12 (1997) · Zbl 0882.47038
[7] Jungck, G.; Rhoades, B. E., Fixed points for set-valued functions without continuity, Indian J. Pure Appl. Math., 29, 3, 227-238 (1998) · Zbl 0904.54034
[8] Pant, R. P., Common fixed points of non-commuting mappings, J. Math. Anal. Appl., 188, 436-440 (1994) · Zbl 0830.54031
[9] Sessa, S., On a weak commutativity condition in fixed point considerations, Publ. Inst. Math., 32, 46, 149-153 (1982) · Zbl 0523.54030
[10] Jungck, G., Compatible mappings and common fixed points, Internat. J. Math. & Math. Sci., 9, 4, 771-779 (1986) · Zbl 0613.54029
[11] Doston, W. G., Fixed point theorems for non-expansive mappings on starshaped subsets of Banach spaces, J. London Math. Soc., 37, 403-410 (1972)
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.