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Generalized Wellposedness and Multivalued Contraction

Year 2014, Volume: 27 Issue: 2, 755 - 759, 27.06.2014

Arockia Prabackar , Ramasamy Uthayakumar

Abstract

In this paper, we establish the fixed point theorem for multivalued contraction. Also we prove that the generalized well posedness of the fixed point problem and continuity of multivalued contraction. 

Keywords

Fixed point; Multivalued mapping; Well-posedness

References

  • Kannan, R Some results on fixed points, Bull. Calcutta Math.Soc. 10 71-76 1968.
  • Kunze, H.E., La Torre, D., and Vrscay, E.R., Contractive multifunctions, fixed point inclusions and iterated multifunction systems, J. Math. Anal. Appl. 330:159-173 2007.
  • Nadler, S.B., Multivalued contraction mappings, Pacific J. Math., 30:475-488 1969.
  • Petrusel A., Rus.I.A, and Cao. J.C, Well-posdeness in the generalized sense of the fixed point problems for multivalued operators, Taiwanese Journal of Mathematics, 11(3) 903-914 2007.
  • Rhoades, B, E., A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc., 226:257-290 1977. [6]. Rhoades, B.E., Contractive continuity, Contemporary Mathematics, 72 233-245 1988. definitions and
  • Rhoades, B.E., Fixed points and continuity for multivalued mappings, Internat. J. Math. Math. Sci., 15 15-30 1992.

Contraction

Year 2014, Volume: 27 Issue: 2, 755 - 759, 27.06.2014

Arockia Prabackar , Ramasamy Uthayakumar

Abstract

References

  • Kannan, R Some results on fixed points, Bull. Calcutta Math.Soc. 10 71-76 1968.
  • Kunze, H.E., La Torre, D., and Vrscay, E.R., Contractive multifunctions, fixed point inclusions and iterated multifunction systems, J. Math. Anal. Appl. 330:159-173 2007.
  • Nadler, S.B., Multivalued contraction mappings, Pacific J. Math., 30:475-488 1969.
  • Petrusel A., Rus.I.A, and Cao. J.C, Well-posdeness in the generalized sense of the fixed point problems for multivalued operators, Taiwanese Journal of Mathematics, 11(3) 903-914 2007.
  • Rhoades, B, E., A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc., 226:257-290 1977. [6]. Rhoades, B.E., Contractive continuity, Contemporary Mathematics, 72 233-245 1988. definitions and
  • Rhoades, B.E., Fixed points and continuity for multivalued mappings, Internat. J. Math. Math. Sci., 15 15-30 1992.
There are 6 citations in total.

Details

Primary Language English
Journal Section Mathematics
Authors

Arockia Prabackar

Ramasamy Uthayakumar

Publication Date June 27, 2014
Published in Issue Year 2014 Volume: 27 Issue: 2

Cite

APA Prabackar, A., & Uthayakumar, R. (2014). Generalized Wellposedness and Multivalued Contraction. Gazi University Journal of Science, 27(2), 755-759.
AMA Prabackar A, Uthayakumar R. Generalized Wellposedness and Multivalued Contraction. Gazi University Journal of Science. June 2014;27(2):755-759.
Chicago Prabackar, Arockia, and Ramasamy Uthayakumar. “Generalized Wellposedness and Multivalued Contraction”. Gazi University Journal of Science 27, no. 2 (June 2014): 755-59.
EndNote Prabackar A, Uthayakumar R (June 1, 2014) Generalized Wellposedness and Multivalued Contraction. Gazi University Journal of Science 27 2 755–759.
IEEE A. Prabackar and R. Uthayakumar, “Generalized Wellposedness and Multivalued Contraction”, Gazi University Journal of Science, vol. 27, no. 2, pp. 755–759, 2014.
ISNAD Prabackar, Arockia - Uthayakumar, Ramasamy. “Generalized Wellposedness and Multivalued Contraction”. Gazi University Journal of Science 27/2 (June 2014), 755-759.
JAMA Prabackar A, Uthayakumar R. Generalized Wellposedness and Multivalued Contraction. Gazi University Journal of Science. 2014;27:755–759.
MLA Prabackar, Arockia and Ramasamy Uthayakumar. “Generalized Wellposedness and Multivalued Contraction”. Gazi University Journal of Science, vol. 27, no. 2, 2014, pp. 755-9.
Vancouver Prabackar A, Uthayakumar R. Generalized Wellposedness and Multivalued Contraction. Gazi University Journal of Science. 2014;27(2):755-9.