Unified Feng-Liu type fixed point theorems solving control problems. (English) Zbl 1502.54048
Summary: The purpose of this work is to study unified Feng-Liu type fixed point theorems using \((\alpha,\eta)\)-muti-valued admissible mappings with more general contraction condition in complete metric spaces. The obtained results generalize and improve several existing theorems in the literature. We use these results in metric spaces endowed with binary relations and partially ordered sets. Some non-trivial example have been presented to illustrate facts and show genuineness of our work. At the end, the established results will be used to obtain existence solutions for a fractional-type integral inclusion.
MSC:
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 54C60 | Set-valued maps in general topology |
| 54E40 | Special maps on metric spaces |
| 54E50 | Complete metric spaces |
References:
| [1] | Nadler, SB, Multi-valued contraction mappings, Pacif. J. Math., 30, 475-488 (1969) · Zbl 0187.45002 · doi:10.2140/pjm.1969.30.475 |
| [2] | Gabeleh, M., Plebaniak, R.: Global optimality results for multivalued non-self mappings in \(b\)-metric spaces. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A. Mat. RACSAM. 112(2), 347-360 (2018) · Zbl 06859075 |
| [3] | Jailoka, P.; Suantai, S., The split common fixed point problem for multivalued demicontractive mappings and its applications, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM, 113, 2, 689-706 (2019) · Zbl 07086841 · doi:10.1007/s13398-018-0496-x |
| [4] | Feng, Y.; Liu, S., Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings, J. Math. Anal. Appl., 317, 103-112 (2006) · Zbl 1094.47049 · doi:10.1016/j.jmaa.2005.12.004 |
| [5] | Nicolae, A., Fixed point theorems for multi-valued mappings of Feng-Liu type, Fixed Point Theory, 12, 1, 145-154 (2011) · Zbl 1281.54035 |
| [6] | Parvaneh, V.; Hussain, N.; Kadelburg, Z., Generalized Wardowski type fixed point theorems via \(\alpha \)-admissible FG-contractions in b-metric spaces, Acta Math. Sci., 36B, 5, 1445-1456 (2016) · Zbl 1374.54056 · doi:10.1016/S0252-9602(16)30080-7 |
| [7] | Wardowski, D., Fixed point theory of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012, 94 (2012) · Zbl 1310.54074 · doi:10.1186/1687-1812-2012-94 |
| [8] | Samet, B.; Vetro, C.; Vetro, P., Fixed-point theorems for \(\alpha -\psi \)-contractive type mappings, Nonlinear Anal., 75, 2154-2165 (2012) · Zbl 1242.54027 · doi:10.1016/j.na.2011.10.014 |
| [9] | Asl, JH; Rezapour, S.; Shahzad, N., On fixed points of \(\alpha -\psi \)-contractive multifunctions, Fixed Point Theory Appl., 2012, 212 (2012) · Zbl 1293.54017 · doi:10.1186/1687-1812-2012-212 |
| [10] | Mohammadi, B.; Rezapour, S.; Shahzad, N., Some results on fixed points of \(\psi \)-Ciric generalized multifunctions, Fixed Point Theory Appl., 2013, 24 (2013) · Zbl 1423.54090 · doi:10.1186/1687-1812-2013-24 |
| [11] | Altun, I.; Minak, G.; Dağ, H., Multivalued \(F\)-contractions on complete metric space, J. Nonlinear Convex Anal., 16, 4, 659-666 (2015) · Zbl 1315.54032 |
| [12] | Altun, I.; Olgun, M.; Minak, G., On a new class of multivalued weakly Picard operators on complete metric spaces, Taiwanese J. Math., 19, 3, 659-672 (2015) · Zbl 1357.54029 · doi:10.11650/tjm.19.2015.4752 |
| [13] | Sahin, H.; Altun, I.; Turkoglu, D., Two fixed point results for multivalued \(F\)-contractions on \(M\)-metric spaces, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM, 113, 3, 1839-1849 (2019) · Zbl 1489.54211 · doi:10.1007/s13398-018-0585-x |
| [14] | Dukić, D.; Kadelburg, Z.; Radenović, S., Fixed points of Geraghty-type mappings in various generalized metric spaces, Abstract Appl. Anal., 561245, 13 (2011) · Zbl 1231.54030 |
| [15] | Minak, G.; Altun, I.; Romaguera, S., Recent developments about multivalued weakly Picard operators, Bull. Belg. Math. Soc. Simon Stevin, 22, 3, 411-422 (2015) · Zbl 1326.54046 · doi:10.36045/bbms/1442364588 |
| [16] | Minak, G.; Olgun, M.; Altun, I., A new approach to fixed point theorems for multivalued mappings, Carpathian J. Math., 31, 2, 241-248 (2015) · Zbl 1349.54111 |
| [17] | Anderson, RD; Ulness, DJ, Newly defined conformable derivatives, Adv. Dyn. Syst. Appl, 10, 2, 109-137 (2015) |
| [18] | Li, Y.; Ang, KH; Chong, GCY, PID control system analysis and design, IEEE Control Syst. Mag., 26, 1, 32-41 (2006) · doi:10.1109/MCS.2006.1580152 |
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