In this paper, we consider the notion of multivalued rational type $ F- $ contraction mappings and prove fixed point theorems for this type mappings. Also we give an illustrative example.
| Citation: |
| [1] |
Ö. Acar, G. Durmaz and G. Minak, Generalized multivalued F-contractions on complete metric space, Bull. Iranian Math. Soc., 40 (2014), 1469-1478.
|
| [2] |
H. Aydi, M.-F. Bota, E. Karapınar and S. Mitrović, A fixed point theorem for set-valued quasi-contractions in b-metric spaces, Fixed Point Theory and Appl., 2012 (2012), 8 pp.
doi: 10.1186/1687-1812-2012-88.
|
| [3] |
H. Baghani, M. E. Gordji and M. Ramezani, Orthogonal sets: The axiom of choice and proof of a fixed-point theorem, J. Fixed Point Theory Appl., 18 (2016) 465–477.
doi: 10.1007/s11784-016-0297-9.
|
| [4] |
I. Beg, G. Mani and A. J. Gnanaprakasam, Fixed point of orthogonal F-Suzuki contraction mapping on $O-$complete metric spaces with applications, Journal of Function Spaces, 2021 (2021), 6692112, 12 pp.
doi: 10.1155/2021/6692112.
|
| [5] |
L. Ćirić, Multi-valued nonlinear contraction mappings, Nonlinear Anal., 71 (2009), 2716-2723.
doi: 10.1016/j.na.2009.01.116.
|
| [6] |
P. Z. Daffer and H. Kaneko, Fixed points of generalized contractive multivalued mappings, J. Math. Anal. Appl., 192 (1995), 655-666.
doi: 10.1006/jmaa.1995.1194.
|
| [7] |
B. K. Dass and S. Gupta, An extension of Banach contraction principle through rational expression, Indian J. Pure Appl. Math., 6 (1975), 1455-1458.
|
| [8] |
M. Eshaghi Gordji and H. Habibi, Fixed point theory in generalized orthogonal metric space, Journal of Linear and Topological Algebra, 6 (2017), 251-260.
|
| [9] |
Y. U. Gaba, E. Karapınar, A. Petruşel and S. Radenovic, New results on start-points for multi-valued maps, Axioms, 9 (2020), 141.
doi: 10.3390/axioms9040141.
|
| [10] |
M. E. Gordji, M. Rameani, M. De La Sen and Y. J. Cho, On orthogon al sets and Banach fixed point theorem, Fixed Point Theory, 18 (2017), 569-578.
doi: 10.24193/fpt-ro.2017.2.45.
|
| [11] |
D. Klim and D. Wardowski, Fixed point theorems for set-valued contractions in complete metric spaces, J. Math. Anal. Appl., 334 (2007), 132-139.
doi: 10.1016/j.jmaa.2006.12.012.
|
| [12] |
S. B. Nadler, Multi-valued contraction mappings, Pacific J. Math., 30 (1969), 475-488.
doi: 10.2140/pjm.1969.30.475.
|
| [13] |
M. Nazam and Ö. Acar, Fixed points of $\left(\alpha, \psi \right) -$contractions in Hausdorff partial metric spaces, Math. Meth. Appl. Sci., 42 (2019), 5159-5173.
doi: 10.1002/mma.5251.
|
| [14] |
M. Nazam, C. Park and M. Arshad, Fixed point problems for generalized contractions with applications, Adv. Differ. Equ., 2021 (2021), No. 247, 15 pp.
doi: 10.1186/s13662-021-03405-w.
|
| [15] |
K. Sawangsup and W. Sintunavarat, Fixed point results for orthogonal $Z-$contraction mappings in $O-$complete metric spaces, Int. J. Appl. Phys. Math., 10 (2020), 33-40.
|
| [16] |
K. Sawangsup, W. Sintunavarat and Y. J. Cho, Fixed point theorems for orthogonal $F-$contraction mappings on $O-$complete metric spaces, J. Fixed Point Theory Appl., 22 (2020), Paper No. 10, 14 pp.
doi: 10.1007/s11784-019-0737-4.
|
| [17] |
R. K. Sharma and S. Chandok, Multivalued problems, orthogonal mappings, and fractional integro-differential equation, Journal of Mathematics, 2020 (2020), 6615478, 8 pp.
doi: 10.1155/2020/6615478.
|
| [18] |
D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012 (2012), 6 pp.
doi: 10.1186/1687-1812-2012-94.
|