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

Year 2019, Volume: 68 Issue: 1, 801 - 808, 01.02.2019

Rqeeb Gubran Walled M. Alfaqıh , Mohammad Imdad

https://doi.org/10.31801/cfsuasmas.478652

Cited By: 1

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

• Wardowski, D., Fixed points of a new type of contractive mappings in complete metric spaces. Fixed Point Theory Appl., Art. ID 94 (2012).
• Górnicki, J., Fixed point theorems for F-expanding mappings. Fixed Point Theory Appl., Art. ID 9 (2017).
• 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.
• 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).
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• Cosentino, M. and Vetro, P., Fixed point results for F-contractive mappings of Hardy-Rogers-type. Filomat, 28(4) (2014), 715--722.
• Durmaz, G., Mınak, G. and Altun, I., Fixed points of ordered F-contractions. Hacettepe Journal of Mathematics and Statistics, 45(1) (2016), 15--21.
• 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.
• Sgroi, M. and Vetro, C., Multi-valued F-contractions and the solution of certain functional and integral equations. Filomat, 27(7) (2013), 1259--1268.
• Wang, S. Z., Some fixed point theorems on expansion mappings. Math. Japon., 29 (1984), 631--636.