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Fixed point of set-valued graph contractions in metric spaces | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 59، دوره 12، شماره 1، مرداد 2021، صفحه 741-747 اصل مقاله (553.5 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.4922 | ||
| نویسندگان | ||
| Masoud Ghods* ؛ Masoud Hadian Dehkordi | ||
| Department of Mathematics, Faculty of Basic Science,Iran University of Science and Technology, Narmak, Tehran,Iran | ||
| تاریخ دریافت: 25 مهر 1394، تاریخ بازنگری: 13 شهریور 1395، تاریخ پذیرش: 28 آذر 1395 | ||
| چکیده | ||
| In this paper, we introduce the (G-$\psi$) contraction in a metric space by using a graph. Let $T$ be a multivalued mappings on $X.$ Among other things, we obtain a fixed point of the mapping $T$ in the metric space $X$ endowed with a graph $G$ such that the set of vertices of $G,$ $V(G)=X$ and the set of edges of $G,$ $E(G)\subseteq X\times X.$ | ||
| کلیدواژه‌ها | ||
| Fixed point؛ multivalued؛ (G-$\psi$) contraction؛ directed graph | ||
| مراجع | ||
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[1] N.A. Assad and W. A. Kirk, Fixed point theorems for set-valued mappings of contractive type, Pacific J. Math. 43 (1972) 533-562. [2] T. G. Bahaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006) 1379-1393. [3] I. Beg and A. Rashid Butt, Fixed point of set-valued graph contractive mappings, J. Inequal. Appl. 2013 (2013) 252. [4] I. Beg, A. Rashid Butt and S. Radojevic, The contraction principle for set-valued mappings on a metric space with a graph, Comput. Math. Appl. 60 (2010) 1214-1219. [5] J. Gross and J. Yellen, Graph Theory and its Applications, CRC Press, 1998. [6] J. Jamchymski, The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc. 136 (2008) 1359-1373. [7] S. B. Nadler, Multivalued contraction mappings, Pacific J. Math. 30 (1969) 475-487. [8] M. Ozturk and E. Girgin, On some fixed-point theorems for ψ-contraction on metric space involving a graph, J. Inequal. Appl. 2014 (2014) 39. [9] A. Petrusel and I. A. Rus, Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc. 134 (2006) 411-418. | ||
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