Compatible mappings of type (B) and common fixed point theorems in Saks spaces

H. K. Pathak; M. S. Khan

Czechoslovak Mathematical Journal (1999)

  • Volume: 49, Issue: 1, page 175-185
  • ISSN: 0011-4642

Abstract

top
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.

How to cite

top

Pathak, H. K., and Khan, M. S.. "Compatible mappings of type (B) and common fixed point theorems in Saks spaces." Czechoslovak Mathematical Journal 49.1 (1999): 175-185. <http://eudml.org/doc/30475>.

@article{Pathak1999,
abstract = {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.},
author = {Pathak, H. K., Khan, M. S.},
journal = {Czechoslovak Mathematical Journal},
keywords = {Saks spaces; compatible mappings of type (A); compatible mappings of type (B); coincidence; common fixed points and compatible mappings; compatible mappings of type (A); coincidence; common fixed points},
language = {eng},
number = {1},
pages = {175-185},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Compatible mappings of type (B) and common fixed point theorems in Saks spaces},
url = {http://eudml.org/doc/30475},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Pathak, H. K.
AU - Khan, M. S.
TI - Compatible mappings of type (B) and common fixed point theorems in Saks spaces
JO - Czechoslovak Mathematical Journal
PY - 1999
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 49
IS - 1
SP - 175
EP - 185
AB - 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.
LA - eng
KW - Saks spaces; compatible mappings of type (A); compatible mappings of type (B); coincidence; common fixed points and compatible mappings; compatible mappings of type (A); coincidence; common fixed points
UR - http://eudml.org/doc/30475
ER -

References

top
  1. The two-norm space, Stud. Math., special vol. (1963), 17–20. (1963) MR0149229
  2. A coincidence theorem and fixed point theorems in Saks spaces, Kobe J. Math. 3 (1986), 1–6. (1986) MR0867797
  3. An approach to fixed points in Saks spaces, Annales dela Soc. Scl. de Bruxelles, T. 9811–III (1984), 80–84. (1984) MR0782739
  4. A common fixed point theorem of Greguš type, Publ. Inst. Math. 34 (1984), 83–89. (1984) MR0901008
  5. 10.1155/S0161171286000030, Internat. J. Math. & Math. Sci. 9 (1986), 23–28. (1986) MR0848231DOI10.1155/S0161171286000030
  6. A coincidence theorem, Bull. Acad. Polon. Sci. Ser. Math. 16 (1968), 733–735. (1968) Zbl0165.49801MR0283648
  7. A fixed point theorem in Banach spaces, Boll. Un. Mat. Ital. 17a (1980), 193–198. (1980) MR0562137
  8. 10.2307/2318216, Amer. Math. Monthly 83 (1976), 261–263. (1976) MR0400196DOI10.2307/2318216
  9. 10.1155/S0161171286000935, Internat. J. Math. and Math. Sci. 9 (1986), 771–779. (1986) MR0870534DOI10.1155/S0161171286000935
  10. 10.1155/S0161171288000341, J. Math. and Math. Sci. 11 (1988), 285–288. (1988) MR0939083DOI10.1155/S0161171288000341
  11. 10.1090/S0002-9939-1988-0947693-2, Proc. Amer. Math. Soc. 103 (1988), 977–983. (1988) MR0947693DOI10.1090/S0002-9939-1988-0947693-2
  12. Compatible mappings of type (A) and common fixed points, Math. Japonica 38 (1993), 381–390. (1993) MR1213401
  13. 10.1155/S0161171289000293, Internat. J. Math. and Math. Sci. 12 (1989), 257–262. (1989) MR0994907DOI10.1155/S0161171289000293
  14. 10.1155/S0161171290000096, Internat. J. Math. and Math. Sci. 13 (1990), 61–66. (1990) MR1038647DOI10.1155/S0161171290000096
  15. Common fixed point theorems, Math. Japonica 37 (1992), 1031–1039. (1992) MR1196378
  16. Single-valued mappings, multi-valued mappings and fixed point theorem in metric spaces, Doctoral Thesis, Garhwal Univ., 1976. (1976) 
  17. A note on a fixed point theorem of Greguš, Math. Japonica 35 (1988), 745–749. (1988) MR0972387
  18. Some fixed point theorems on Saks spaces, Bull. Cal. Math. Soc. 84 (1992), 289–293. (1992) MR1210602
  19. Coincidence points, common fixed points and compatible maps of type (A) on Saks spaces, Preprint. 
  20. Coincidence theorems, Preprint. 
  21. Compatible mappings of type (B) and common fixed pont theorems of Greguš type, Czechoslovak Math. J. 45(120) (1995), 685–698. (1995) MR1354926
  22. Coincidence theorems on L -spaces, Math. Japonica 28 (1981), 291–295. (1981) Zbl0471.54034MR0624218
  23. 10.4064/sm-11-1-237-272, Stud. Math. 11 (1950), 237–272. (1950) MR0038556DOI10.4064/sm-11-1-237-272
  24. 10.4064/sm-15-1-1-25, Stud. Math. 15 (1955), 1–25. (1955) MR0073942DOI10.4064/sm-15-1-1-25
  25. Some results on Saks spaces, Stud. Math. 16 (1957), 16–68. (1957) MR0094686
  26. On a weak commutativity of mappings in fixed point consideratons, Publ. Inst. Math. 32(46) (1982), 149–153. (1982) MR0710984
  27. Coincidence theorems on 2-metric spaces, Indian J. Phy. Math. Sci. 2(B) (1982), 32–35. (1982) 
  28. 10.1017/S000497270002298X, Bull. Austral. Math. Soc. 16 (1977), 49–53. (1977) MR0438318DOI10.1017/S000497270002298X

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.