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A common fixed point theorem via measure of noncompactness | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 22، دوره 12، شماره 2، بهمن 2021، صفحه 293-296 اصل مقاله (291.03 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2017.10595.1513 | ||
| نویسندگان | ||
| Alireza Valipour Baboli1؛ Mohammad Bagher Ghaemi* 2 | ||
| 1Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran | ||
| 2Department of Mathematics, Iran University of Science and Technology, Tehran, Iran | ||
| تاریخ دریافت: 24 آذر 1395، تاریخ بازنگری: 15 دی 1394، تاریخ پذیرش: 30 بهمن 1395 | ||
| چکیده | ||
| In this paper by applying the measure of noncompactness a common fixed point for the maps $T$ and $S$ is obtained, where $T$ and $S$ are self maps continuous or commuting continuous on a closed convex subset $C$ of a Banach space $E$ and also $S$ is a linear map. | ||
| کلیدواژهها | ||
| Common fixed point theorem؛ The Kuratowski measure of noncompactness؛ Commuting map؛ Darbo's contraction conditions | ||
| مراجع | ||
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[1] R.P. Agarwal and D. O’Regan, Fixed Point Theory and Applications, Cambridge University Press, (2004). [2] A. Aghajani, R. Allahyari and M. Mursaleen, A generalization of Darbo’s theorem with application to the solvability of systems of integral equations, J. Comput Appl. Math. 260 (2014) 680–770. [3] A. Aghajani, J. Banas and N.Sabzali, Some generalization of Darbo fixed point theorem and applications,Bull. Belg. Math. Soc.Simon Sterin, 20(2) (2013) 345–358. [4] A. Aghajani, M. Mursaleen and A.Shole Haghighi, Fixed point theorems fFor Meir-Keeler condensing operators via measure of nNoncompactness, Acta Math. Sci. 35B(3) (2015) 552–566. [5] A. Aghajani, N. Sabzali, Existence of coupled fixed points via measure of noncompactness and applications, J. Nonlinear Convex Anal. 15(5) (2015). [6] R. R. Akmerov, M. I. Kamenski, A. S. Potapov, A. E. Rodkina and B. N. Sadovskii, Measures of Noncompactness and Condensing Operators, Birkhauser-Verlag, Basel, 1992. [7] S. Banach, Surles op´erations dans les ensembles abstraits et leurs applications aux ´equations int´egrales, Fund. Math. 3 (1922) 137–181. [8] J. Banas and K. Goebel, Measure of Noncompactness in Banach Space, Lecture Notes in Pure and Applied Mathematics, vol. 60, Marcel Dekker, New York, 1980. [9] G. Darbo, Punti uniti in trasformazioni a codominio non compatto, Rend Sem Mat Univ Padova, 24 (1955) 84–92. [10] K. Kuratowski, Sur les espaces, Fund. Math. 15 (1930) 301–309. | ||
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