doi: 10.3934/mfc.2022026
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Multivalued rational type F-contraction on orthogonal metric space

Department of Mathematics, Faculty of Science, Selçuk University, 42003, Konya, Turkey

*Corresponding author: Özlem Acar

Dedicated to occasion of 60th birthday of Prof. Vijay Gupta

Received  April 2022 Revised  May 2022 Early access July 2022

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: Özlem Acar, Aybala Sevde Özkapu. Multivalued rational type F-contraction on orthogonal metric space. Mathematical Foundations of Computing, doi: 10.3934/mfc.2022026
References:
[1]

Ö. AcarG. 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. GabaE. KarapınarA. Petruşel and S. Radenovic, New results on start-points for multi-valued maps, Axioms, 9 (2020), 141.  doi: 10.3390/axioms9040141.

[10]

M. E. GordjiM. RameaniM. 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.

show all references

References:
[1]

Ö. AcarG. 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. GabaE. KarapınarA. Petruşel and S. Radenovic, New results on start-points for multi-valued maps, Axioms, 9 (2020), 141.  doi: 10.3390/axioms9040141.

[10]

M. E. GordjiM. RameaniM. 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.

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