Best proximity point results in partially ordered metric spaces via simulation functions. (English) Zbl 1338.90324
Summary: We obtain sufficient conditions for the existence and uniqueness of best proximity points for a new class of non-self mappings involving simulation functions in a metric space endowed with a partial order. Some interesting consequences including fixed point results via simulation functions are presented.
MSC:
| 90C26 | Nonconvex programming, global optimization |
| 47H10 | Fixed-point theorems |
| 06A06 | Partial orders, general |
References:
| [1] | Khojasteh, F, Shukla, S, Radenović, S: A new approach to the study of fixed point theory for simulation functions. Filomat 29(6), 1189-1194 (2015) · Zbl 1462.54072 · doi:10.2298/FIL1506189K |
| [2] | Argoubi, H, Samet, B, Vetro, C: Nonlinear contractions involving simulation functions in a metric space with a partial order. J. Nonlinear Sci. Appl. 8, 1082-1094 (2015) · Zbl 1328.54030 |
| [3] | Du, WS, Khojasteh, F: New results and generalizations for approximate fixed point property and their applications. Abstr. Appl. Anal. 2014, Article ID 581267 (2014) · Zbl 1474.54151 |
| [4] | Du, WS, Khojasteh, F, Chiu, YN: Some generalizations of Mizoguchi-Takahashi’s fixed point theorem with new local constraints. Fixed Point Theory Appl. 2014, 31 (2014) · Zbl 1328.54037 · doi:10.1186/1687-1812-2014-31 |
| [5] | Khojasteh, F, Karapinar, E, Radenović, S: Metric space: a generalization. Math. Probl. Eng. 2013, Article ID 504609 (2013) · Zbl 1296.54033 · doi:10.1155/2013/504609 |
| [6] | Roldán-López-de-Hierro, AF, Karapinar, E, Roldán-López-de-Hierro, C, Martínez-Moreno, J: Coincidence point theorems on metric spaces via simulation functions. J. Comput. Appl. Math. 275, 345-355 (2015) · Zbl 1318.54034 · doi:10.1016/j.cam.2014.07.011 |
| [7] | Roldán-López-de-Hierro, AF, Shahzad, N: New fixed point theorem under R-contractions. Fixed Point Theory Appl. 2015, 98 (2015) · Zbl 1462.54095 · doi:10.1186/s13663-015-0345-y |
| [8] | Abkar, A, Gabeleh, M: Best proximity points for cyclic mappings in ordered metric spaces. J. Optim. Theory Appl. 150(1), 188-193 (2011) · Zbl 1232.54035 · doi:10.1007/s10957-011-9810-x |
| [9] | Basha, SS: Discrete optimization in partially ordered sets. J. Glob. Optim. 54(3), 511-517 (2012) · Zbl 1261.90039 · doi:10.1007/s10898-011-9774-2 |
| [10] | Bilgili, N, Karapinar, E, Sadarangani, K: A generalization for the best proximity point of Geraghty-contractions. J. Inequal. Appl. 2013, 286 (2013) · Zbl 1281.54020 · doi:10.1186/1029-242X-2013-286 |
| [11] | de la Sen, M, Agarwal, RP: Some fixed point-type results for a class of extended cyclic self-mappings with a more general contractive condition. Fixed Point Theory Appl. 2011, 59 (2011) · Zbl 1315.54034 · doi:10.1186/1687-1812-2011-59 |
| [12] | Eldred, AA, Veeramani, P: Existence and convergence of best proximity points. J. Math. Anal. Appl. 323(2), 1001-1006 (2006) · Zbl 1105.54021 · doi:10.1016/j.jmaa.2005.10.081 |
| [13] | Jleli, M, Karapinar, E, Samet, B: A best proximity point result in modular spaces with the Fatou property. Abstr. Appl. Anal. 2013, Article ID 329451 (2013) · Zbl 1325.41019 |
| [14] | Jleli, M, Karapinar, E, Samet, B: A short note on the equivalence between best proximity points and fixed point results. J. Inequal. Appl. 2014, 246 (2014) · Zbl 1308.41034 · doi:10.1186/1029-242X-2014-246 |
| [15] | Jleli, M, Samet, B: An optimization problem involving proximal quasi-contraction mappings. Fixed Point Theory Appl. 2014, 141 (2014) · Zbl 1349.54106 · doi:10.1186/1687-1812-2014-141 |
| [16] | Karapinar, E: Fixed point theory for cyclic weak ϕ-contraction. Appl. Math. Lett. 24(6), 822-825 (2011) · Zbl 1256.54073 · doi:10.1016/j.aml.2010.12.016 |
| [17] | Karapinar, E, Pragadeeswarar, V, Marudai, M: Best proximity point for generalized proximal weak contractions in complete metric space. J. Appl. Math. 2014, Article ID 150941 (2014) · Zbl 1406.54026 |
| [18] | Kim, WK, Lee, KH: Existence of best proximity pairs and equilibrium pairs. J. Math. Anal. Appl. 316(2), 433-446 (2006) · Zbl 1101.47040 · doi:10.1016/j.jmaa.2005.04.053 |
| [19] | Kirk, WA, Reich, S, Veeramani, P: Proximinal retracts and best proximity pair theorems. Numer. Funct. Anal. Optim. 24(7-8), 851-862 (2003) · Zbl 1054.47040 · doi:10.1081/NFA-120026380 |
| [20] | Nashine, HK, Kumam, P, Vetro, C: Best proximity point theorems for rational proximal contractions. Fixed Point Theory Appl. 2013, 95 (2013) · Zbl 1295.41038 · doi:10.1186/1687-1812-2013-95 |
| [21] | Raj, VS: A best proximity point theorem for weakly contractive non-self-mappings. Nonlinear Anal. 74(14), 4804-4808 (2011) · Zbl 1228.54046 · doi:10.1016/j.na.2011.04.052 |
| [22] | Srinivasan, PS, Veeramani, P: On existence of equilibrium pair for constrained generalized games. Fixed Point Theory Appl. 2004(1), 21-29 (2004) · Zbl 1091.47060 · doi:10.1155/S1687182004308132 |
| [23] | Pragadeeswarar, V, Marudai, M: Best proximity points for generalized proximal weak contractions satisfying rational expression on ordered metric spaces. Abstr. Appl. Anal. 2015, Article ID 361657 (2015) · Zbl 1351.54030 · doi:10.1155/2015/361657 |
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