Common fixed points of generalized contractive hybrid pairs in symmetric spaces. (English) Zbl 1185.54038

Summary: Several fixed point theorems for hybrid pairs of single-valued and multivalued occasionally weakly compatible maps satisfying generalized contractive conditions are established in a symmetric space.


54H25 Fixed-point and coincidence theorems (topological aspects)
54E25 Semimetric spaces
54C60 Set-valued maps in general topology
Full Text: DOI EuDML


[1] Kannan R: Some results on fixed points.Bulletin of the Calcutta Mathematical Society 1968, 60: 71-76. · Zbl 0209.27104
[2] Sessa S: On a weak commutativity condition of mappings in fixed point considerations.Publications de l’Institut Mathématique. Nouvelle Série 1982, 32(46): 149-153. · Zbl 0523.54030
[3] Jungck G: Compatible mappings and common fixed points.International Journal of Mathematics and Mathematical Sciences 1986,9(4):771-779. 10.1155/S0161171286000935 · Zbl 0613.54029 · doi:10.1155/S0161171286000935
[4] Jungck G: Common fixed points for noncontinuous nonself maps on nonmetric spaces.Far East Journal of Mathematical Sciences 1996,4(2):199-215. · Zbl 0928.54043
[5] Al-Thagafi MA, Shahzad N: Generalized -nonexpansive selfmaps and invariant approximations.Acta Mathematica Sinica 2008,24(5):867-876. 10.1007/s10114-007-5598-x · Zbl 1175.41026 · doi:10.1007/s10114-007-5598-x
[6] Jungck G, Rhoades BE: Fixed point theorems for occasionally weakly compatible mappings.Fixed Point Theory 2006,7(2):287-296. · Zbl 1118.47045
[7] Zhang X: Common fixed point theorems for some new generalized contractive type mappings.Journal of Mathematical Analysis and Applications 2007,333(2):780-786. 10.1016/j.jmaa.2006.11.028 · Zbl 1133.54028 · doi:10.1016/j.jmaa.2006.11.028
[8] Abbas M, Rhoades BE: Common fixed point theorems for hybrid pairs of occasionally weakly compatible mappings defined on symmetric spaces.Panamerican Mathematical Journal 2008,18(1):55-62. · Zbl 1152.54030
[9] Abbas M, Rhoades BE: Common fixed point theorems for occasionally weakly compatible mappings satisfying a generalized contractive condition.Mathematical Communications 2008,13(2):295-301. · Zbl 1175.47050
[10] Aliouche A: A common fixed point theorem for weakly compatible mappings in symmetric spaces satisfying a contractive condition of integral type.Journal of Mathematical Analysis and Applications 2006,322(2):796-802. 10.1016/j.jmaa.2005.09.068 · Zbl 1111.47046 · doi:10.1016/j.jmaa.2005.09.068
[11] Chandra H, Bhatt A: Some fixed point theorems for set valued maps in symmetric spaces.International Journal of Mathematical Analysis 2009,3(17):839-846. · Zbl 1196.54065
[12] Cho, S-H; Lee, G-Y; Bae, J-S, On coincidence and fixed-point theorems in symmetric spaces, 9 (2008) · Zbl 1169.54020
[13] Hicks TL, Rhoades BE: Fixed point theory in symmetric spaces with applications to probabilistic spaces.Nonlinear Analysis: Theory, Methods & Applications 1999,36(3):331-344. 10.1016/S0362-546X(98)00002-9 · Zbl 0947.54022 · doi:10.1016/S0362-546X(98)00002-9
[14] Imdad M, Ali J: Common fixed point theorems in symmetric spaces employing a new implicit function and common property (E.A).Bulletin of the Belgian Mathematical Society. Simon Stevin 2009, 16: 421-433. · Zbl 1188.47044
[15] Pathak HK, Tiwari R, Khan MS: A common fixed point theorem satisfying integral type implicit relations.Applied Mathematics E-Notes 2007, 7: 222-228. · Zbl 1178.54023
[16] Beg, I.; Abbas, M., Coincidence point and invariant approximation for mappings satisfying generalized weak contractive condition, 7 (2006) · Zbl 1133.54024
[17] Chang TH: Common fixed point theorems for multivalued mappings.Mathematica Japonica 1995,41(2):311-320. · Zbl 0840.47041
[18] Shrivastava PK, Bawa NPS, Nigam SK: Fixed point theorems for hybrid contractions.Varāhmihir Journal of Mathematical Sciences 2002,2(2):275-281. · Zbl 1033.54523
[19] Azam A, Beg I: Coincidence points of compatible multivalued mappings.Demonstratio Mathematica 1996,29(1):17-22. · Zbl 0862.54039
[20] Kamran T: Common coincidence points of R -weakly commuting maps.International Journal of Mathematics and Mathematical Sciences 2001,26(3):179-182. 10.1155/S0161171201005245 · Zbl 1006.54061 · doi:10.1155/S0161171201005245
[21] Jungck G, Rhoades BE: Fixed points for set valued functions without continuity.Indian Journal of Pure and Applied Mathematics 1998,29(3):227-238. · Zbl 0904.54034
[22] Hadžić O: Common fixed point theorems for single-valued and multivalued mappings.Review of Research. Faculty of Science. Mathematics Series 1988,18(2):145-151. · Zbl 0729.54032
[23] Kaneko H, Sessa S: Fixed point theorems for compatible multi-valued and single-valued mappings.International Journal of Mathematics and Mathematical Sciences 1989,12(2):257-262. 10.1155/S0161171289000293 · Zbl 0671.54023 · doi:10.1155/S0161171289000293
[24] Kaneko H: A common fixed point of weakly commuting multi-valued mappings.Mathematica Japonica 1988,33(5):741-744. · Zbl 0664.54031
[25] Fisher B: Common fixed points for set-valued mappings.Indian Journal of Mathematics 1983,25(3):265-270. · Zbl 0573.54039
[26] Sessa S, Fisher B: On common fixed points of weakly commuting mappings and set-valued mappings.International Journal of Mathematics and Mathematical Sciences 1986,9(2):323-329. 10.1155/S0161171286000406 · Zbl 0593.54051 · doi:10.1155/S0161171286000406
[27] Fisher B: Common fixed point theorem for commutative mappings and set valued mappings.Journal of University of Kuwait 1984, 11: 15-21. · Zbl 0549.54032
[28] Dhage BC: Common fixed point theorems for coincidentally commuting pairs of nonself mappings in metrically convex metric spaces.Analele Ştiinţifice ale Universităţii Al. I. Cuza din Iaşi. Serie Nouă. Matematică 2003,49(1):45-60. · Zbl 1073.47522
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