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Fixed point uniqueness of generalized $(\psi , \varphi)$-weak contractions in partially ordered metric spaces under suitable constraints | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 21، دوره 15، شماره 2، اردیبهشت 2024، صفحه 255-262 اصل مقاله (359.95 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.25883.3151 | ||
| نویسنده | ||
| Gholamreza Heidary Joonaghany* | ||
| Department of Mathematics, Arak Branch, Islamic Azad University, Arak, Iran | ||
| تاریخ دریافت: 21 آبان 1400، تاریخ بازنگری: 14 دی 1400، تاریخ پذیرش: 23 دی 1400 | ||
| چکیده | ||
| In this paper, by providing an example, we show that the condition which produced by Radenovi'{c} and Kadelburg in [Generalized weak contractions in partially ordered metric spaces, Comput. Math. Appl. 60 (2010) pp. 1776-1783] is not sufficient for the uniqueness of the fixed point. Furthermore, a new sufficient condition is introduced for the uniqueness of the fixed point. Some suitable examples are furnished to demonstrate the validity of the hypotheses of our results. | ||
| کلیدواژهها | ||
| Fixed point؛ Generalized $(\psi؛ \phi)$-Weak Contraction؛ Ordered metric space | ||
| مراجع | ||
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[1] D. -Doric, Common fixed point for generalized (ψ −φ)-weak contraction, Appl. Math. Lett. 22 (2009), 1896–1900. [2] J. Harjani and K. Sadarangani, Fixed point theorems for weakly contractive mappings in partially ordered sets, Nonlinear Anal. 71 (2009), 3403–3410. [3] M. Jovanovic, Z. Kadelburg and S. Radenovic, Common fixed point results in metric-type spaces, Fixed Point Theory Appl. 2010 (2010), Article ID 978121, 15 pages. [4] G. Jungck, Common fixed points for noncontinuous nonself maps on non-metric spaces, Far East J. Math. Sci. 4 (1996), 199–215. [5] Z. Kadelburg, M. Pavlovic and S. Radenovic, Common fixed point theorems for ordered contractions and quasicontractions in ordered cone metric spaces, Comput. Math. Appl. 59 (2010), 3148–3159. [6] J.J. Nieto and R. Rodriguez-Lopez, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005), 223–239. [7] J.J. Nieto and R. Rodriguez-Lopez, Existence and uniqueness of fixed points in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. Engl. Ser. 23 (2007), 2205–2212. [8] D. ORegan and A. Petrusel, Fixed point theorems for generalized contractions in ordered metric spaces, J. Math. Anal. Appl. 341 (2008), 1241–1252. [9] S. Radenovic and Z. Kadelburg, Generalized weak contractions in partially ordered metric spaces, Comput. Math. Appl. 60 (2010), 1776–1783. [10] S. Radenovic, Z. Kadelburg, D. Jandrlic and A. Jandrlic, Some results on weakly contractive maps, Bull. Iran. Math. Soc. 38 (2012), no. 3, 625–645. [11] A.C.M. Ran and M.C.B. Reurings, A fixed point theorem in partially ordered sets and some application to matrix equations, Proc. Amer. Math. Soc. 132 (2004), 1435–1443. [12] Q. Zhang and Y. Song, Fixed point theory for generalized (ψ−φ)-weak contractions, Appl. Math. Lett. 22 (2009), 75–78. | ||
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