jaem

TWMS Journal of Applied and Engineering Mathematics

2146-1147 2587-1013

Işık University Press

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

Shukla

Satish

Department of Applied Mathematics, Shri Vaishnav Institute of Technology & Science Gram Baroli, Road, Indore (M.P.) 453331, India.

12 01 2016

6 2 342 353

2010

TWMS Journal of Applied and Engineering Mathematics

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.

F-contraction partial rectangular metric space fixed point graph.

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.