Previous |  Up |  Next

Article

Keywords:
Saks spaces; compatible mappings of type (A); compatible mappings of type (B); coincidence; common fixed points and compatible mappings
Summary:
In this paper we first introduce the concept of compatible mappings of type (B) and compare these mappings with compatible mappings and compatible mappings of type (A) in Saks spaces. In the sequel, we derive some relations between these mappings. Secondly, we prove a coincidence point theorem and common fixed point theorem for compatible mappings of type (B) in Saks spaces.
References:
[1] A. Alexiewicz: The two-norm space. Stud. Math., special vol. (1963), 17–20. MR 0149229
[2] Y. J. Cho and S. L. Singh: A coincidence theorem and fixed point theorems in Saks spaces. Kobe J. Math. 3 (1986), 1–6. MR 0867797
[3] Y. J. Cho and S. L. Singh: An approach to fixed points in Saks spaces. Annales dela Soc. Scl. de Bruxelles, T. 9811–III (1984), 80–84. MR 0782739
[4] M. L. Divicaro, B. Fisher and S. Sessa: A common fixed point theorem of Greguš type. Publ. Inst. Math. 34 (1984), 83–89. MR 0901008
[5] B. Fisher and S. Sessa: On a common fixed point theorem of Greguš. Internat. J. Math. & Math. Sci. 9 (1986), 23–28. DOI 10.1155/S0161171286000030 | MR 0848231
[6] K. Goebel: A coincidence theorem. Bull. Acad. Polon. Sci. Ser. Math. 16 (1968), 733–735. MR 0283648 | Zbl 0165.49801
[7] M. Greguš: A fixed point theorem in Banach spaces. Boll. Un. Mat. Ital. 17a (1980), 193–198. MR 0562137
[8] G. Jungck: Commuting maps and fixed points. Amer. Math. Monthly 83 (1976), 261–263. DOI 10.2307/2318216 | MR 0400196
[9] G. Jungck: Compatible and common fixed points. Internat. J. Math. and Math. Sci. 9 (1986), 771–779. DOI 10.1155/S0161171286000935 | MR 0870534
[10] G. Jungck: Compatible mappings and common fixed points (2), Internat. J. Math. and Math. Sci. 11 (1988), 285–288. DOI 10.1155/S0161171288000341 | MR 0939083
[11] G. Jungck: Common fixed points of commuting and compatible maps on compacta. Proc. Amer. Math. Soc. 103 (1988), 977–983. DOI 10.1090/S0002-9939-1988-0947693-2 | MR 0947693
[12] G. Jungck, P. P. Murthy and Y. J. Cho: Compatible mappings of type (A) and common fixed points. Math. Japonica 38 (1993), 381–390. MR 1213401
[13] H. Kaneko and S. Sessa: Fixed point theorems for compatible multivalued mappings. Internat. J. Math. and Math. Sci. 12 (1989), 257–262. DOI 10.1155/S0161171289000293 | MR 0994907
[14] S. M. Kang, Y. J. Cho and G. Jungck: Common fixed points of compatible mappings. Internat. J. Math. and Math. Sci. 13 (1990), 61–66. DOI 10.1155/S0161171290000096 | MR 1038647
[15] S. M. Kang and Y. P. Kim: Common fixed point theorems. Math. Japonica 37 (1992), 1031–1039. MR 1196378
[16] G. C. Kulshrestha: Single-valued mappings, multi-valued mappings and fixed point theorem in metric spaces. Doctoral Thesis, Garhwal Univ., 1976.
[17] R. N. Mukherjee and V. Verma: A note on a fixed point theorem of Greguš. Math. Japonica 35 (1988), 745–749. MR 0972387
[18] P. P. Murthy and B. K. Sharma: Some fixed point theorems on Saks spaces. Bull. Cal. Math. Soc. 84 (1992), 289–293. MR 1210602
[19] P. P. Murphy and B. K. Sharma and Y. J. Cho: Coincidence points, common fixed points and compatible maps of type (A) on Saks spaces. Preprint.
[20] S. A. Naimpally, S. L. Singh and J. H. M. Whitfield: Coincidence theorems. Preprint.
[21] H. K. Pathak and M. S. Khan: Compatible mappings of type (B) and common fixed pont theorems of Greguš type. Czechoslovak Math. J. 45(120) (1995), 685–698. MR 1354926
[22] T. Okada: Coincidence theorems on $L$-spaces. Math. Japonica 28 (1981), 291–295. MR 0624218 | Zbl 0471.54034
[23] W. Orlicz: Linear operators in Saks spaces (I). Stud. Math. 11 (1950), 237–272. DOI 10.4064/sm-11-1-237-272 | MR 0038556
[24] W. Orlicz: Linear operators in Saks (II). Stud. Math. 15 (1955), 1–25. DOI 10.4064/sm-15-1-1-25 | MR 0073942
[25] W. Orlicz and V. Pták: Some results on Saks spaces. Stud. Math. 16 (1957), 16–68. MR 0094686
[26] S. Sessa: On a weak commutativity of mappings in fixed point consideratons. Publ. Inst. Math. 32(46) (1982), 149–153. MR 0710984
[27] S. L. Singh and Virendra: Coincidence theorems on 2-metric spaces. Indian J. Phy. Math. Sci. 2(B) (1982), 32–35.
[28] S. P. Singh and B. A. Meade: On common fixed point theorems. Bull. Austral. Math. Soc. 16 (1977), 49–53. DOI 10.1017/S000497270002298X | MR 0438318
Partner of
EuDML logo