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Fixed point theorems for Reich type contractions on metric spaces with a graph. (English) Zbl 1250.54044
The paper presents a fixed point theorem for so-called Reich type operators in metric spaces endowed with a connected graph. The result generalize some recent results of this type given by J. Jachymski in [“The contraction principle for mappings on a metric space with a graph”, Proc. Am. Math. Soc. 136, No. 4, 1359–1373 (2008; Zbl 1139.47040)].
##### MSC:
 54H25 Fixed-point and coincidence theorems in topological spaces 05C40 Connectivity 54E40 Special maps on metric spaces 54E50 Complete metric spaces
##### References:
 [1] Petruşel, A.; Rus, I. A.: Fixed point theorems in ordered L-spaces, Proc. amer. Math. soc. 134, 411-418 (2006) · Zbl 1086.47026 · doi:10.1090/S0002-9939-05-07982-7 [2] Johnsonbaugh, R.: Discrete math., (1997) [3] Jachymski, J.: The contraction principle for mappings on a metric space with a graph, Proc. amer. Math. soc. 1, No. 136, 1359-1373 (2008) · Zbl 1139.47040 · doi:10.1090/S0002-9939-07-09110-1 [4] Bega, I.; Butt, A. R.; Radojević, S.: The contraction principle for set valued mappings on a metric space with a graph, Comput. math. Appl. 60, 1214-1219 (2010) · Zbl 1201.54029 · doi:10.1016/j.camwa.2010.06.003 [5] Bojor, F.: Fixed point of $\phi$-contraction in metric spaces endowed with a graph, Ann. univ. Craiova math. Comput. sci. Ser. 37, No. 4, 85-92 (2010) · Zbl 1215.54018 [6] Reich, S.: Fixed points of contractive functions, Boll. unione mat. Ital. 5, 26-42 (1972) · Zbl 0249.54026 [7] Ćirić, L. B.: A generalization of Banach’s contraction principle, Proc. amer. Math. soc. 45, 267-273 (1974) · Zbl 0291.54056 · doi:10.2307/2040075 [8] Rus, I. A.; Petruşel, A.; Petruşel, G.: Fixed point theory, (2008) [9] Petric, M. A.: Some remarks concerning ciric-reich-rus operators, Creat. math. Inform. 18, No. 2, 188-193 (2009)