Common Fixed Point Theorems of Self
Mappings in non-Newtonian Metric Spaces

Demet Binbasioglu

doi:https://doi.org/10.14445/22315373/IJMTT-V67I3P506

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 67 | Issue 3 | Year 2021 | Article Id. IJMTT-V67I3P506 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I3P506

Common Fixed Point Theorems of Self Mappings in non-Newtonian Metric Spaces

Demet Binbasioglu

Abstract

The non-Newtonian metric concept was defined in 2012 [5], and then the non-Newtonian metric spaces and their some topological properties were gived by Binbasioglu, Demiriz, Turkoglu in 2016 [6]. Also, they introduced the fixed point theory in non-Newtonian metric spaces. In this paper, we proved some common fixed point theorems and results for self mappings in the non-Newtonian metric spaces.

Keywords

Common fixed point theorem, Contraction mapping, Fixed point theorem, Non-Newtonian calculi, Non- Newtonian metric space

References

[1] M. Abbas, G. Jungck., Common fixed point results for non-commuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl., 341 (2008) 416-420.
[2] I. Altun, D. Turkoglu., Some fixed point theorems for weakly compatible mappings satisfying an implicit relation, Taiwanese J. Math., 13 (4) (2009) 1291-1304.
[3] I. Altun, D. Turkoglu, B.E. Rhoades., Fixed points of weakly compatible maps satisfying a general contractive condition of integral type, Fixed Point Theory Appl., Art. ID 17301, (2007) 9 .
[4] I. Altun and C. Cevik., Some common fixed point theorems in vector metric spaces., Filomat, 25(1) (2011) 105-113.
[5] D. Binbasioglu, S. Demiriz, D. Turkoglu., Fixed Points of non-Newtonian Contraction Mappings on non-Newtonian Metric Spaces, J. Fixed Point Theory Appl. 18 (2016) 213–224.
[6] A. F. Cakmak, F. Basar., Some New Results on a Sequence Spaces with Respect to non-Newtonian Calculus, Journal of Inequalities and Appl., 1 (2012) 228.
[7] C. C¸ evik, I. Altun., Vector metric spaces and some properties, Topol. Met. Nonlin. Anal., (2) (2009) 375-382.
[8] L.-G. Huang, X. Zhang., Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007) 1468-1476.
[9] G. Jungck, S. Radenovic, S. Radojevic, V. Rakocevic., Common fixed point theorems for weakly compatible pairs on cone metric spaces, Fixed Point Theory Appl., Art. ID 643840, (2009) 13.
[10] M. Kirisci., Topological Structures of non-Newtonian Metric Spaces, Electronic Journal of Mathematical Analysis and Applications, 5 (2) (2017) 156-169.
[11] S. Radenovi´c, V. Rakoˇcevi´c, S. Resapour., Common fixed points for (g, f) type maps in cone metric spaces, Applied Mathematics and Computation, 218 (2011) 480–491.

Citation :

Demet Binbasioglu, "Common Fixed Point Theorems of Self Mappings in non-Newtonian Metric Spaces," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 3, pp. 45-50, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I3P506