Browse > Article
http://dx.doi.org/10.5831/HMJ.2017.39.2.161

SOME NEW COMMON FIXED POINTS OF GENERALIZED RATIONAL CONTRACTIVE MAPPINGS IN DISLOCATED METRIC SPACES WITH APPLICATION  

Khan, Sami Ullah (Department of Mathematics, International Islamic University)
Arshad, Muhammad (Department of Mathematics, International Islamic University)
Rasham, Tahair (Department of Mathematics, International Islamic University)
Shoaib, Abdullah (Department of Mathematics, Ripha International University)
Publication Information
Honam Mathematical Journal / v.39, no.2, 2017 , pp. 161-174 More about this Journal
Abstract
The objective of this manuscript is to continue the study of fixed point theory in dislocated metric spaces, introduced by Hitzler et al. [12]. Concretely, we apply the concept of dislocated metric spaces and obtain theorems asserting the existence of common fixed points for a pair of mappings satisfying new generalized rational contractions in such spaces.
Keywords
Common fixed point; Dislocated metric; Contractive type mappings;
Citations & Related Records
연도 인용수 순위
  • Reference
1 M. Abbas, B. E. Rhoades, Fixed and periodic point results in cone metric spaces. Appl. Math. Lett. 22. 511-515 (2009)   DOI
2 M. Arshad, A. Azam, M. Abbas, A. Shoaib, Fixed point results of dominated mappings on a closed ball in ordered partial metric spaces without continuity, U.P.B. Sci. Bull., Series A, Vol. 76, Iss.2. 2014.
3 M. Arshad, E. Karapinar, J. Ahmad, Some Unique Fixed Point Theorem For Rational Contractions in Partially Ordered Metric Spaces, Journal of Inequalities and Applications, 2013.
4 M. Arshad, S.U. Khan, HK, Nashine, M. Nazam, Some Common Fixed Points of Generalized Contractive Mappings on Complex Valued Metric Spaces, J. Ana. Num. Theory. 5, No. 1, 73-80 (2017).   DOI
5 J. Ahmad, N. Hussain, New Suzuki-Berinde Type Fixed Point Results, CARPATHIAN J. MATH, 33 (2017), No. 1, 59-72.
6 S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations int egrales, Fund. Math., 3 (1922), 133-181.   DOI
7 A. Branciari, A fixed point theorem of Banach-Caccippoli type on a class of generalized metric spaces, Public. Math. Debrecen 57 31-37 (2000).
8 B. C. Dhage, Generalized metric spaces with fixed point. Bull. Calcutta Math. Soc. 84, 329-336 (1992).
9 C. E. Frechet, Surquelques points du calcul fonctionnal, Rendiconti del Circolo Mathematico di Palermo, vol 22, 2nd semester. pp 1-74 (1906).   DOI
10 A. Al-Rawashdeh, J. Ahmad, Common Fixed Point Theorems for JS-Contractions, Bulletin of Mathematical Analysis and Applications Volume 8 Issue 4(2016), Pages 12-22.
11 L. G. Haung, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings. J. Math. Anal. Appl. 332, 1468-1476 (2007).   DOI
12 P. Hitzler, A. K. Seda, Dislocated topologies. J. Electr. Eng. 51(12), 3-7 (2000).
13 P. Hitzler, Generalized metrics and topology in logic programming semantics. PhD thesis, National University of Ireland (University College, Cork) (2001).
14 S.G. Matthews, Partial metric topology Proc. 8th Summer Conference on General Topology and Applications, Ann. New York Acad. Sci.,vol. 728, 1994, pp. 183-197.
15 W. A. Kirk, Some recent results in metric fixed point theory, J. Fixed point theory and appl. 2, 195-207 (2007).   DOI
16 MA. Kutbi, J. Ahmad, N. Hussain, M. Arshad, Common Fixed Point Results for Mappings with Rational Expressions, Abstract and Applied Analysis vol. 2013, Article ID 549518, 11 pages.
17 S. Oltra, O. Valero, Banach fixed point theorems for partial metric spaces, Rend. Ist. Mat. Univ, Trieste 36(2004), 17-26.
18 SJ. O'Neill, Partial metrics, valuations and domain theory Proc. 11th Summer Conference on General Topology and Applications, Ann. New York Acad. Sci, vol. 806, 1996, pp. 304-315.
19 S. Radenovic, B. E. Rhoades, Fixed point theorem for two non-self mappings in cone metric spaces. Comput. Math. Appl. 57 1701-1707 (2009).   DOI
20 S. Rezapour, R. Hamlbarani, Some notes on the paper 'cone metric spaces and fixed point theorems of contractive mappings'. J. Math. Anal. Appl. 345 719-724 (2008).   DOI
21 S. Romaguera and M. Schellekens, Quasi-metric properties of complexity spaces Topology Appl. 98(1999), 311-322.   DOI
22 M. Arshad, S. U. Khan, J. Ahmad, Fixed point results for F-contractions involving some new rational expressions, JP Journal of Fixed Point Theory and Applications Volume 11, Number 1, 2016, Pages 79-97.   DOI
23 S. U. Khan, and Arjamand Bano, Common fixed point theorems for f-contraction mappings in TVS-valued cone metric spaces, J. of New Theory, 2016, Number13, Pages: 96-103.
24 C. Semple, M. Steel, Phylogenetics, Oxford Lecture Ser. In Math Appl, vol. 24, Oxford Univ. Press, Oxford (2003).
25 O. Valero, On Banach fixed point theorems for partial metric spaces, Applied General Topology, Vol.6, No.2, 2005.