Browse > Article
http://dx.doi.org/10.4134/CKMS.c160127

COINCIDENCE THEOREMS FOR COMPARABLE GENERALIZED NON LINEAR CONTRACTIONS IN ORDERED PARTIAL METRIC SPACES  

Dimri, Ramesh Chandra (Department of Mathematics H.N.B. Garhwal University)
Prasad, Gopi (H.N.B. Garhwal University)
Publication Information
Communications of the Korean Mathematical Society / v.32, no.2, 2017 , pp. 375-387 More about this Journal
Abstract
In this paper, we prove some coincidence point theorems involving ${\varphi}-contraction$ in ordered partial metric spaces. We also extend newly introduced notion of g-comparability of a pair of maps for linear contraction in ordered metric spaces to non-linear contraction in ordered partial metric spaces. Thus, our results extend, modify and generalize some recent well known coincidence point theorems of ordered metric spaces.
Keywords
ordered partial metric space; g-comparable mappings; ICU property; TCC property;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 R. P. Agarwal, M. A. El-Gebeily, and D. O'Regan, Generalized contractions in partially ordered metric spaces, Appl. Anal. 87 (2008), no. 1, 109-116.   DOI
2 A. Alam and M. Imdad, Comparable linear contractions in ordered metric spaces, Fixed Point Theory, in press.
3 A. Alam and M. Imdad, Monotone generalized contractions in ordered metric spaces, Bull. Korean Math. Soc. 53 (2016), no. 1, 61-81.   DOI
4 A. Alam, A. R. Khan, and M. Imdad, Some coincidence theorems for genralized nonlinear contractions in ordered metric spaces with applications, Fixed Point Theory Appl. 2014 (2014), 216, 30 pp.   DOI
5 I. Altun and A. Erduran, Fixed point theorems for monotone mappings on partial metric spaces, Fixed Point Theory Appl. 2011 (2011), Article ID 508730, 10 pp.   DOI
6 I. Altun and H. Simsek, Some fixed point theorems on ordered metric spaces and applications, Fixed Point Theory Appl. 2010 (2010), Article ID 621469, 17 pp.
7 I. Altun, F. Sola, and H. Simsek, Generalized contractions on partial metric spaces. Topology Appl. 157 (2010), no. 18, 2778-2785.   DOI
8 D. W. Boyd and J. S. W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc. 20 (1969), 458-464.   DOI
9 M. Bukatin, R. Kopperman, S. Matthews, and H. Pajoohesh, Partial metric spaces, Amer. Math. Monthly 116 (2009), no. 8, 708-718.   DOI
10 M. A. Bukatin and S. Yu. Shorina, Partial metrics and co-continuous valuations, In: Ni-vat M, et al. (eds.) Foundations of software science and computation structures (Lisbon, 1998), 125-139, Lecture Notes in Comput. Sci., 1378, Springer, Berlin, 1998.
11 L. Ciri'c, N. Cakic, M. Rajovic, and J. S. Ume, Monotone generalized nonlinear contractions in partially ordered metric spaces, Fixed Point Theory Appl. 2008 (2008), Art. ID 131294, 11 pp.
12 S. G. Matthews, Partial metric topology, In Proceedings of the 8th Summer Conference on General Topology and Applications, pp. 183-197, Ann. New York Acad. Sci., 728, New York Acad. Sci., New York, 1994.   DOI
13 N. Joti'c, Some fixed point theorems in metric spaces, Indian J. Pure Appl. Math. 26 (1995), no. 10, 947-952.
14 G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci. 9 (1986), no. 4, 771-779.   DOI
15 V. Lakshmikantham and L. Ciri'c, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. 70 (2009), no. 12, 4341-4349.   DOI
16 S. G. Matthews, An extensional treatment of lazy data on deadlock, Theoret. Comput. Sci. 151 (1995), no. 1, 195-205.   DOI
17 D. O'Regan and A. Petrusel, Fixed point theorems for generalized contractions in ordered metric spaces, J. Math. Anal. Appl. 341 (2008), no. 2, 1241-1252.   DOI
18 A. Mukherjea, Contractions and completely continuous mappings, Nonlinear Anal. 1 (1977), no. 3, 235-247.   DOI
19 J. J. Nieto and R. Rodriguez-Lopez, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005), no. 3, 223-239.   DOI
20 J. J. Nieto and R. Rodriguez-Lopez, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sinica 23 (2007), no. 12, 2205-2212.   DOI
21 S. Romaguera, A Kirk type characterization of completeness for partial metric spaces, Fixed Point Theory Appl. 2010 (2010), Article ID 493298, 6 pp.
22 S. Oltra and O. Valero, Banach's fixed point theorem for partial metric spaces, Rend. Istit. Mat. Univ. Trieste 36 (2004), no. 1-2, 17-26.
23 S. Radenovic and Z. Kadelburg, Generalized weak contractions in partially ordered metric spaces, Comput. Math. Appl. 60 (2010), no. 6, 1776-1783.   DOI
24 A. C. M. Ran and M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004), no. 5, 1435-1443.   DOI
25 I. A. Rus, Fixed point theory in partial metric spaces, An. Univ. Vest. Timis. Ser. Mat.-Inform. 46 (2008), no. 2, 149-160.
26 J. J. M. M. Rutten, Weighted colimits and formal balls in generalized metric spaces, Topology Appl. 89 (1998), no. 1-2, 179-202.   DOI
27 S. Samet, M. Rajovic, R. Lazovic, and R. Stojiljkovic, Common fixed point results for nonlinear contractions in ordered partial metric spaces, Fixed Point Theory Appl. 2011 (2011), 71, 14 pp.   DOI
28 M. Turinici, Nieto-Lopez theorems in ordered metric spaces, Math. Student 81 (2012), no. 1-4, 219-229.
29 M. Turinici, Abstract comparison principles and multivariable Gronwall-Bellman inequalities, J. Math. Anal. Appl. 117 (1986), no. 1, 100-127.   DOI
30 M. Turinici, Fixed points for monotone iteratively local contractions, Demonstr. Math. 19 (1986), no. 1, 171-180.
31 O. Valero, On Banach fixed point theorems for partial metric spaces, Appl. Gen. Topol. 6 (2005), no. 2, 229-240.   DOI
32 M. Turinici, Ran-Reurings fixed point results in ordered metric spaces, Libertas Math. 31 (2011), 49-55.