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FIXED POINTS OF CONTRACTIVE SET VALUED MAPPINGS WITH SET VALUED DOMAINS ON A METRIC SPACE WITH GRAPH

Yıl 2014, Cilt: 4 Sayı: 2, 169 - 174, 01.12.2014

Öz

In this article we consider general contractive mappings of the form F : CB X → CB X , where CB X is the set of all nonempty closed and bounded subsets of a complete metric space X endowed with a graph G. We prove some fixed point results for F and discuss how the connectivity of the graph G is related to the fixed points of F.

Kaynakça

  • Aleomraninejad, S. M. A., Rezapour, Sh., and Shahzad, N., (2012), Some Şxed point results on a metric space with a graph, Topology Appl., 159, 659-663.
  • Assad, N. A., and Kirk, W. A., (1972), Fixed point theorems for set-valued mappings of contractive type, PaciŞc J. Math. 43(3), 553-561.
  • Beg, I., Butt, A. R., and Radojevic, S., (2010), The contraction principle for set valued mappings on a metric space with a graph, Comput. Math. Appl., 60, 1214-1219.
  • Espinola, R., and Kirk, W. A., (2006), Fixed point theorems in R-trees with applications to graph theory, Topology Appl., 153, 1046-1055.
  • Gwozdz-Lukawska, G., and Jachymski, J., (2009), IFS on a metric space with a graph structure and extensions of the Kelisky-Rivlin theorem, J. Math. Anal. Appl., 356, 453-463.
  • Harary, F., (1972), Graph theory, 3rd Edition, Addison-Wesley, Reading, MA.
  • Jachymski, J., (2007), The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc., 136(4), 1359-1373.
  • Nadler, S. B., (1969), Multi-valued contraction mappings, PaciŞc J. Math., 30(2), 475-488.
  • Nieto, J. J., Pouso, R. L., and Rodriguez-Lopez, R., (2007), Fixed point theorems in ordered abstract spaces, Proc. Amer. Math. Soc., 135, 2505-2517.
  • Nieto, J. J., and Rodriguez-Lopez, R., (2007), Existence and uniqueness of Şxed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sinica English Ser., 2205
  • Petrusel, A., and Rus, I. A., (2006), Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc. 134, 411-418.
  • Ran, A. C. M., and Reurings, M. C. B., (2004), A Şxed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 132, 1435-1443.
Yıl 2014, Cilt: 4 Sayı: 2, 169 - 174, 01.12.2014

Öz

Kaynakça

  • Aleomraninejad, S. M. A., Rezapour, Sh., and Shahzad, N., (2012), Some Şxed point results on a metric space with a graph, Topology Appl., 159, 659-663.
  • Assad, N. A., and Kirk, W. A., (1972), Fixed point theorems for set-valued mappings of contractive type, PaciŞc J. Math. 43(3), 553-561.
  • Beg, I., Butt, A. R., and Radojevic, S., (2010), The contraction principle for set valued mappings on a metric space with a graph, Comput. Math. Appl., 60, 1214-1219.
  • Espinola, R., and Kirk, W. A., (2006), Fixed point theorems in R-trees with applications to graph theory, Topology Appl., 153, 1046-1055.
  • Gwozdz-Lukawska, G., and Jachymski, J., (2009), IFS on a metric space with a graph structure and extensions of the Kelisky-Rivlin theorem, J. Math. Anal. Appl., 356, 453-463.
  • Harary, F., (1972), Graph theory, 3rd Edition, Addison-Wesley, Reading, MA.
  • Jachymski, J., (2007), The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc., 136(4), 1359-1373.
  • Nadler, S. B., (1969), Multi-valued contraction mappings, PaciŞc J. Math., 30(2), 475-488.
  • Nieto, J. J., Pouso, R. L., and Rodriguez-Lopez, R., (2007), Fixed point theorems in ordered abstract spaces, Proc. Amer. Math. Soc., 135, 2505-2517.
  • Nieto, J. J., and Rodriguez-Lopez, R., (2007), Existence and uniqueness of Şxed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sinica English Ser., 2205
  • Petrusel, A., and Rus, I. A., (2006), Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc. 134, 411-418.
  • Ran, A. C. M., and Reurings, M. C. B., (2004), A Şxed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 132, 1435-1443.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

P. Debnath Bu kişi benim

Yayımlanma Tarihi 1 Aralık 2014
Yayımlandığı Sayı Yıl 2014 Cilt: 4 Sayı: 2

Kaynak Göster