A Related Fixed Point Theorem for $F$-Contractions on Two Metric Spaces

Year 2019, Volume: 48 Issue: 1, 150 - 156, 01.02.2019

Murat Olgun , Özge Biçer , Tuğçe Alyıldız İshak Altun

https://izlik.org/JA95CD42GX

Abstract

Recently, Wardowski in [Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 2012] introduced the concept of $F$-contraction on complete metric space which is a proper generalization of Banach contraction principle. In the present paper, we proved a related fixed point theorem with $F$-contraction mappings on two complete metric spaces.

Keywords

fixed point , $F$-Contractions , complete metric space

References

• A. Aliouche and B. Fisher, A related fixed point theorem for two pairs of mappings on two complete metric spaces, Hacet. J. Math. Stat. 34, 39-45, 2005.
• I. Altun, G. Durmaz, G. Mınak and S. Romaguera, Multivalued almost $F$-contractions on complete metric spaces, Filomat 30 (2), 441-448, 2016.
• B. Fisher, Fixed points on two metric spaces, Glas. Mat. Ser. III 16 (36), 333-337, 1981.
• B. Fisher, Related fixed points on two metric spaces, Math. Sem. Notes Kobe Univ. 10, 17-26, 1982.
• B. Fisher, R.K. Jain and H.K. Sahu, Related fixed point theorems for three metric spaces, Novi Sad J. Math. 26 (1), 11-17, 1996.
• M. Imdad, R. Gubran, M. Arif and D. Gopal, An observation on $\alpha$-type $F$-contractions and some ordered-theoretic fixed point results, Math. Sci. 11 (3), 247-255, 2017.
• G. Mınak, A. Helvacı and I. Altun, Ciric type generalized $F$-contractions on complete metric spaces and fixed point results, Filomat 28 (6), 1143-1151, 2014.
• G. Mınak, M. Olgun and I. Altun, A new approach to fixed point theorems for multivalued contractive maps, Carpathian J. Math. 31 (2), 241-248, 2015.
• R.K. Namdeo, D. Gupta and B. Fisher, A related fixed point theorem on two metric spaces, Punjab Univ. J. Math. 27, 109-112, 1994.
• R.K. Namdeo, S. Jain and B. Fisher, A related fixed point theorem for two pairs of mappings on two complete metric spaces, Hacet. J. Math. Stat. 32, 7-11, 2013.
• M. Olgun, G. Mınak and I. Altun, A new approach to Mizoguchi-Takahashi type fixed point theorems, J. Nonlinear Convex Anal. 17 (3), 579-587, 2016.
• H. Piri and P. Kumam, Some fixed point theorems concerning $F$-contraction in complete metric spaces, Fixed Point Theory Appl. 2014, 210, 2014.
• M. Sgrio and C. Vetro, Multi-valued $F$-contractions and the solution of certain functional and integral equations, Filomat 27 (7), 1259-1268, 2013.
• D. Singh, V. Joshi, M. Imdad and P. Kumam, Fixed point theorems via generalized $F$-contractions with applications to functional equations occurring in dynamic programming, J. Fixed Point Theory Appl. 19 (2), 1453-1479, 2017.
• F. Vetro, F-contractions of Hardy-Rrogers type and application to multistage decision processes, Nonlinear Anal. Model. Control 21 (4), 531-546, 2016.
• D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 2012, 94, 2012.
• D.Wardowski and N.V. Dung, Fixed points of $F$-weak contractions on complete metric spaces, Demonstratio Math. 47 (1), 146-155, 2014.