Best proximity points in noncommutative Banach spaces. (English) Zbl 1489.54077
Summary: This paper introduces the concept of \(k\)-ordered proximal contractions and then [we] study best proximity point results for these mappings. An example is given to show accuracy and significance of our claims.
MSC:
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 41A65 | Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) |
| 46L52 | Noncommutative function spaces |
Keywords:
best proximity point; proximal comparable; noncommutative Banach space; ordered contractive conditionReferences:
| [1] | Aleksić, S.; Kadelburg, Z.; Mitrović, ZD; Radenović, S., A new survey: cone metric spaces, J Int Math Virtual Inst, 9, 93-121 (2019) · Zbl 1474.54102 |
| [2] | Altun, I.; Aslantas, M.; Sahin, H., Best proximity point results for p-proximal contractions, Acta Math Hung, 162, 393-402 (2020) · Zbl 1474.54107 · doi:10.1007/s10474-020-01036-3 |
| [3] | Altun, I.; Aslantas, M.; Sahin, H., KW-Type nonlinear contractions and their best proximity points, Numer Funct Anal Optim, 24, 1-20 (2021) · Zbl 1473.54044 |
| [4] | Altun, I.; Damnjanovic, B.; Djoric, D., Fixed point and common fixed point theorems on ordered cone metric spaces, Appl Math Lett, 23, 310-316 (2010) · Zbl 1197.54052 · doi:10.1016/j.aml.2009.09.016 |
| [5] | Aslantas, M.; Sahin, H.; Altun, I., Best proximity point theorems for cyclic p-contractions with some consequences and applications, Nonlinear Anal Model Control, 26, 1, 113-129 (2021) · Zbl 1476.54052 · doi:10.15388/namc.2021.26.21415 |
| [6] | Banach, S., Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund Math, 3, 1, 133-181 (1922) · JFM 48.0201.01 · doi:10.4064/fm-3-1-133-181 |
| [7] | Basha, SS, Best proximity points: optimal solutions, J Optim Theory Appl, 151, 210-216 (2011) · Zbl 1226.90135 · doi:10.1007/s10957-011-9869-4 |
| [8] | Cho, YJ; Saadati, R.; Wang, SH, Common fixed point theorems on generalized distance in ordered cone metric spaces, Comput Math Appl, 61, 1254-1260 (2011) · Zbl 1217.54041 · doi:10.1016/j.camwa.2011.01.004 |
| [9] | Chung, KJ, Nonlinear contractions in abstract spaces, Kodai Math J, 4, 288-292 (1981) · Zbl 0469.47043 · doi:10.2996/kmj/1138036375 |
| [10] | Chung, KJ, Remarks on nonlinear contractions, Pac J Math, 101, 41-48 (1982) · Zbl 0459.54033 · doi:10.2140/pjm.1982.101.41 |
| [11] | Du, WS, A note on cone metric fixed point theory and its equivalence, Nonlinear Anal Theory Methods Appl, 72, 2259-2261 (2010) · Zbl 1205.54040 · doi:10.1016/j.na.2009.10.026 |
| [12] | Du, WS, New cone fixed point theorems for nonlinear multivalued maps with their applications, Appl Math Lett, 24, 172-178 (2011) · Zbl 1218.54037 · doi:10.1016/j.aml.2010.08.040 |
| [13] | Eldered, AA; Veeramani, P., Existence and convergence for best proximity points, J Math Anal Appl, 33, 1001-1006 (2006) · Zbl 1105.54021 · doi:10.1016/j.jmaa.2005.10.081 |
| [14] | Fabiano N et al (2021) Solving fractional differential equations using fixed point results in generalized metric spaces of Perov’s type. In press, TWMS App and Eng Math |
| [15] | Huang, LG; Zhang, X., Cone metric spaces and fixed point theorems of contractive mappings, J Math Anal Appl, 33, 2, 1468-1476 (2007) · Zbl 1118.54022 · doi:10.1016/j.jmaa.2005.03.087 |
| [16] | Janković, S.; Kadelburg, Z.; Radenović, S., On cone metric spaces: a survey, Nonlinear Anal Theory Methods Appl, 74, 2591-2601 (2011) · Zbl 1221.54059 · doi:10.1016/j.na.2010.12.014 |
| [17] | Kadelburg, Z.; Pavlović, M.; Radenović, S., Common fixed point theorems for ordered contractions and quasicontractions in ordered cone metric spaces, Comput Math Appl, 59, 9, 3148-3159 (2010) · Zbl 1193.54035 · doi:10.1016/j.camwa.2010.02.039 |
| [18] | Kurepa, DR, Tableaux ramifi Ìes densembles. Espaces pseudo-distanci Ìes, C R Math Acad Sci Paris, 198, 1563-1565 (1934) · Zbl 0009.13205 |
| [19] | Proinov, PD, A unified theory of cone metric spaces and its applications to the fixed point theory, Fixed Point Theory Appl, 1, 1-38 (2013) · Zbl 1294.54035 |
| [20] | Raj, VS, A best proximity point theorem for weakly contractive non-self-mappings, Nonlinear Anal Theory Methods Appl, 74, 14, 4804-4808 (2011) · Zbl 1228.54046 · doi:10.1016/j.na.2011.04.052 |
| [21] | Raj, VS, Best proximity point theorems for nonself mappings, Fixed Point Theory, 14, 2, 447-454 (2013) · Zbl 1280.41026 |
| [22] | Sahin, H.; Aslantas, M.; Altun, I., Feng-Liu type approach to best proximity point results for multivalued mappings, J Fixed Point Theory Appl, 22, 1, 1-13 (2020) · Zbl 1431.54039 · doi:10.1007/s11784-019-0740-9 |
| [23] | Savić, A.; Fabiano, N.; Mirkov, N.; Sretenović, A.; Radenovi, S., Some significant remarks on multivalued Perov type contractions on cone metric spaces with a directed graph, AIMS Math, 7, 1, 187-198 (2022) · Zbl 1485.54058 · doi:10.3934/math.2022011 |
| [24] | Sultana, A.; Vetrivel, V., On the existence of best proximity points for generalized contractions, Appl Gen Topol, 15, 1, 55-63 (2014) · Zbl 1297.54109 · doi:10.4995/agt.2014.2221 |
| [25] | Xin, Q.; Jiang, L., Fixed-point theorems for mappings satisfying the ordered contractive condition on noncommutative spaces, Fixed Point Theory Appl, 2014, 30 (2014) · Zbl 1390.47010 · doi:10.1186/1687-1812-2014-30 |
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