Random fixed points of multivalued maps in Fréchet spaces

Naseer Shahzad

Archivum Mathematicum (2002)

  • Volume: 038, Issue: 2, page 95-100
  • ISSN: 0044-8753

Abstract

top
In this paper we prove a general random fixed point theorem for multivalued maps in Frechet spaces. We apply our main result to obtain some common random fixed point theorems. Our main result unifies and extends the work due to Benavides, Acedo and Xu [4], Itoh [8], Lin [12], Liu [13], Tan and Yuan [20], Xu [23], etc.

How to cite

top

Shahzad, Naseer. "Random fixed points of multivalued maps in Fréchet spaces." Archivum Mathematicum 038.2 (2002): 95-100. <http://eudml.org/doc/248925>.

@article{Shahzad2002,
abstract = {In this paper we prove a general random fixed point theorem for multivalued maps in Frechet spaces. We apply our main result to obtain some common random fixed point theorems. Our main result unifies and extends the work due to Benavides, Acedo and Xu [4], Itoh [8], Lin [12], Liu [13], Tan and Yuan [20], Xu [23], etc.},
author = {Shahzad, Naseer},
journal = {Archivum Mathematicum},
keywords = {multivalued map; random fixed point; Frechet space; multivalued map; random fixed point; Fréchet space},
language = {eng},
number = {2},
pages = {95-100},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Random fixed points of multivalued maps in Fréchet spaces},
url = {http://eudml.org/doc/248925},
volume = {038},
year = {2002},
}

TY - JOUR
AU - Shahzad, Naseer
TI - Random fixed points of multivalued maps in Fréchet spaces
JO - Archivum Mathematicum
PY - 2002
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 038
IS - 2
SP - 95
EP - 100
AB - In this paper we prove a general random fixed point theorem for multivalued maps in Frechet spaces. We apply our main result to obtain some common random fixed point theorems. Our main result unifies and extends the work due to Benavides, Acedo and Xu [4], Itoh [8], Lin [12], Liu [13], Tan and Yuan [20], Xu [23], etc.
LA - eng
KW - multivalued map; random fixed point; Frechet space; multivalued map; random fixed point; Fréchet space
UR - http://eudml.org/doc/248925
ER -

References

top
  1. Beg I., Shahzad N., Some random approximation theorems with applications, Nonlinear Anal. 35 (1999), 609–616. (1999) Zbl0931.60054MR1656922
  2. Beg I., Shahzad N., Random fixed points of weakly inward operators in conical shells, J. App. Math. Stochastic Anal. 8 (1995), 261–264. (1995) Zbl0828.47044MR1342645
  3. Beg I., Shahzad N., Applications of the proximity map to random fixed point theorems in Hilbert spaces, J. Math. Anal. Appl. 196 (1995), 606–613. (196) MR1362709
  4. Benavides T. D., Acedo G. L., Xu H. K., Random fixed points of set-valued operators, Proc. Amer. Math. Soc. 124 (1996), 831–838. (1996) Zbl0841.47032MR1301487
  5. Bharucha-Reid A. T., Fixed point theorems in probabilistic analysis, Bull. Amer. Math. Soc. 82 (1976), 641–657. (1976) Zbl0339.60061MR0413273
  6. Browder F. E., Semicontractive and semiaccretive nonlinear mappings in Banach spaces, Bull. Amer. Math. Soc. 74 (1968), 660–665. (1968) Zbl0164.44801MR0230179
  7. Himmelberg C. J., Measurable relations, Fund. Math. 87 (1975), 53–72. (1975) Zbl0296.28003MR0367142
  8. Itoh S., Random fixed point theorems with an application to random differential equations in Banach spaces, J. Math. Anal. Appl. 67 (1979), 261–273. (1979) Zbl0407.60069MR0528687
  9. Itoh S., A random fixed point theorem for a multivalued contraction mapping, Pacific J. Math. 68 (1977), 85–90. (1977) Zbl0335.54036MR0451228
  10. Kuratowski K., Ryll-Nardzewski C., A general theorem on selectors, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 13 (1965), 379–403. (1965) Zbl0152.21403MR0188994
  11. Lami Dozo E., Multivalued nonexpansive mappings with Opial’s condition, Proc. Amer. Math. Soc. 38 (1973), 286–292. (1973) MR0310718
  12. Lin T. C., Random approximations and random fixed point theorems for continuous 1-set-contractive random maps, Proc. Amer. Math. Soc. 123 (1995), 1167–1176. (1995) Zbl0834.47049MR1227521
  13. Liu L. S., Some random approximations and random fixed point theorems for 1-set-contractive random operators, Proc. Amer. Math. Soc. 125 (1997), 515–521. (1997) Zbl0869.47031MR1350953
  14. Opial Z., Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 595–597. (1967) Zbl0179.19902MR0211301
  15. Papageorgiou N. S., Random fixed points and random differential inclusions, Int. J. Math. Math. Sci. 11 (1988), 551–560. (1988) Zbl0658.60090MR0947287
  16. Rudin W., Functional Analysis, McGraw Hill, New York, 1973. (1973) Zbl0253.46001MR0365062
  17. Shahzad N., Random fixed point theorems for various classes of 1-set-contractive maps in Banach spaces, J. Math. Anal. Appl. 203 (1996), 712–718. (1996) Zbl0893.47037MR1417125
  18. Shahzad N., Khan L. A., Random fixed points for 1-set-contractive random maps in Frechet spaces, J. Math. Anal. Appl. 231 (1999), 68–75. (1999) MR1676737
  19. Shahzad N., Latif S., Random fixed points for several classes of 1-ball-contractive and 1-set-contractive random maps, J. Math. Anal. Appl. 237 (1999), 83–92. (1999) Zbl1115.47314MR1708163
  20. Tan K. K., Yuan X. Z., Random fixed point theorems and approximation, Stochastic Anal. Appl. 15 (1997), 103–123. (1997) Zbl0892.47060MR1429860
  21. Tan K. K., Yuan X. Z., Random fixed point theorems and approximation in cones, J. Math. Anal. Appl. 185 (1994), 378–390. (1994) Zbl0856.47036MR1283065
  22. Thomas G. E. F., Integration on functions with values in locally convex Suslin spaces, Trans. Amer. Math. Soc. 212 (1975), 61–81. (1975) MR0385067
  23. Xu H. K., Some random fixed point theorems for condensing and nonexpansive operators, Proc. Amer. Math. Soc. 110 (1990), 495–500. (1990) Zbl0716.47029MR1021908
  24. Xu H. K., Beg I., Measurability of fixed point sets of multivalued random operators, J. Math. Anal. Appl. 225 (1998), 62–72. (1998) Zbl0913.47057MR1639289

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.