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G- F;  -CONTRACTIONS IN PARTIAL RECTANGULAR METRIC SPACES ENDOWED WITH A GRAPH AND FIXED POINT THEOREMS

Yıl 2016, Cilt: 6 Sayı: 2, 342 - 353, 01.12.2016

Öz

In this paper, the notion of G- F;  -contractions in the context of partial rectangular metric spaces endowed with a graph is introduced. Some xed point theorems for G- F;  -contractions are also proved. The results of this paper generalize, extend, and unify some known results. Some examples are provided to illustrate the results proved herein.

Kaynakça

  • Branciari,A., (2000), A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen, 57 1-2, pp. 31-37.
  • Wardowski,D., (2012), Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory and Applications, pp. 94.
  • Boyd,D.W. and Wong,J.S.W., (1969), On nonlinear contractions, Proceedings of the American Math- ematical Society, 20(2), pp. 458-464.
  • Jachymski,J., (2008), The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc., 136, pp. 1359-1373.
  • Ciri´c,L.B., (1974), A generalization of Banachs contraction principle, Proc Amer. Math. Soc., 45, pp. 73.
  • Ciri´c,L.B., (1971), Generalized contractions and fxed-point theorems, Publ. lInst Math. (Beograd), , pp. 19-26.
  • Fr´echet,M., (1906), Sur quelques points du calcul fonctionnel, Rendiconti Circolo Mat. Palermo, 22, pp. 1-74.
  • Edelstein,M., (1961), An extension of Banach’s contraction principle, Proc. Amer. Math. Soc., 12, MR 22 #11375, pp. 7-10.
  • Banach,S., (1922), Sur les op´erations dans les ensembles abstraits et leur application aux ´equations int´egrales, Fundamenta Mathematicae, 3, pp. 133-181.
  • Matthews,S.G., (1994), Partial metric topology, in: Proc. 8th Summer Conference on General Topol- ogy and Application, Ann. New York Acad. Sci., 728, pp. 183-197.
  • Shukla,S., (2014), Partial rectangular metric spaces and fixed point theorems, The ScientificWorld Journal, 2014, Article ID 756298, pp. 7.
  • Suzuki,T., (2008), A generalized Banach contraction principle that characterizes metric completeness, Proceedings of the American Mathematical Society, 136(5), pp. 1861-1869.
Yıl 2016, Cilt: 6 Sayı: 2, 342 - 353, 01.12.2016

Öz

Kaynakça

  • Branciari,A., (2000), A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen, 57 1-2, pp. 31-37.
  • Wardowski,D., (2012), Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory and Applications, pp. 94.
  • Boyd,D.W. and Wong,J.S.W., (1969), On nonlinear contractions, Proceedings of the American Math- ematical Society, 20(2), pp. 458-464.
  • Jachymski,J., (2008), The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc., 136, pp. 1359-1373.
  • Ciri´c,L.B., (1974), A generalization of Banachs contraction principle, Proc Amer. Math. Soc., 45, pp. 73.
  • Ciri´c,L.B., (1971), Generalized contractions and fxed-point theorems, Publ. lInst Math. (Beograd), , pp. 19-26.
  • Fr´echet,M., (1906), Sur quelques points du calcul fonctionnel, Rendiconti Circolo Mat. Palermo, 22, pp. 1-74.
  • Edelstein,M., (1961), An extension of Banach’s contraction principle, Proc. Amer. Math. Soc., 12, MR 22 #11375, pp. 7-10.
  • Banach,S., (1922), Sur les op´erations dans les ensembles abstraits et leur application aux ´equations int´egrales, Fundamenta Mathematicae, 3, pp. 133-181.
  • Matthews,S.G., (1994), Partial metric topology, in: Proc. 8th Summer Conference on General Topol- ogy and Application, Ann. New York Acad. Sci., 728, pp. 183-197.
  • Shukla,S., (2014), Partial rectangular metric spaces and fixed point theorems, The ScientificWorld Journal, 2014, Article ID 756298, pp. 7.
  • Suzuki,T., (2008), A generalized Banach contraction principle that characterizes metric completeness, Proceedings of the American Mathematical Society, 136(5), pp. 1861-1869.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

Satish Shukla Bu kişi benim

Yayımlanma Tarihi 1 Aralık 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 6 Sayı: 2

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