Fixed point results for F-expansive mappings in ordered metric spaces

Abstract

In this article, we prove some existence and uniqueness fixed point results for F-expansive mappings in partially ordered metric spaces. We support the usability of our results adopting suitable examples.

Keywords

• Fixed point,F-contraction,F-expansive mapping

References

1. Wardowski, D., Fixed points of a new type of contractive mappings in complete metric spaces. Fixed Point Theory Appl., Art. ID 94 (2012).
2. Górnicki, J., Fixed point theorems for F-expanding mappings. Fixed Point Theory Appl., Art. ID 9 (2017).
3. Ran, A. C. M. and Reurings, M. C. B., A fixed point theorem in partially ordered sets and some applications to matrix equations. Proc. Am. Math. Soc., 132(5) (2004), 1435--1443.
4. Alam, A., Khan, A-R and Imdad, M., Some coincidence theorems for generalized nonlinear contractions in ordered metric spaces with applications. Fixed Point Theory Appl., Art. ID 216 (2014).
5. Ćirić, L., Abbas, M., Saadati, R. and Hussain, H., Common fixed points of almost generalized contractive mappings in ordered metric spaces. Applied Mathematics and Computation, 217(12) (2011), 5784--5789.
6. Gubran, R. and Imdad, M., Results on coincidence and common fixed points for (ψ, ϕ) g-generalized weakly contractive mappings in ordered metric spaces. Mathematics, 4 (68) (2016), 1--13.
7. Imdad, M., Gubran, R. and Ahmadullah, Md., Using an implicit function to prove common fixed point theorems. J.Adv.Math.Stud, 11(3) (2018), 481-495.
8. Imdad, M. and Gubran, R., Ordered-theortic fixed point results for monotone generalized Boyd-Wong and Matkowski type contractions. J. Adv. Mat. Stud., 10(1) (2017), 49--61.

9. Nashine, H. K. and Altun, I., A common fixed point theorem on ordered metric spaces. Bulletin of the Iranian Mathematical Society, 38(4) (2012), 925--934.
10. Nieto, J. J. and Rodríguez-López, R., Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations. Order, 22(3) (2005), 223--239.
11. Nieto, J. J. and Rodríguez-López, R., Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations. Acta Math. Sin. (Engl. Ser.), 23(12) (2007), 2205--2212.
12. O'Regan, D. and Petruşel, A., Fixed point theorems for generalized contractions in ordered metric spaces. J. Math. Anal. Appl, 341(2) (2008), 1241--1252.
13. Abbas, M., Ali, B. and Romaguera, S., Fixed and periodic points of generalized contractions in metric spaces. Fixed Point Theory Appl., Art. ID:243:1--11, 2013.
14. Cosentino, M. and Vetro, P., Fixed point results for F-contractive mappings of Hardy-Rogers-type. Filomat, 28(4) (2014), 715--722.
15. Durmaz, G., Mınak, G. and Altun, I., Fixed points of ordered F-contractions. Hacettepe Journal of Mathematics and Statistics, 45(1) (2016), 15--21.
16. Imdad, M., Gubran, R., Arif, M. and Gopal, D., An observation on α-type F-contractions and some ordered-theoretic fixed point results. Mathematical Sciences, 11(3) (2017), 247--255.
17. Sgroi, M. and Vetro, C., Multi-valued F-contractions and the solution of certain functional and integral equations. Filomat, 27(7) (2013), 1259--1268.
18. Wang, S. Z., Some fixed point theorems on expansion mappings. Math. Japon., 29 (1984), 631--636.