Common fixed point of mappings satisfying implicit contractive conditions in TVS-valued ordered cone metric spaces
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Authors
Hemant Kumar Nashine
- Department of Mathematics, Disha Institute of Management and Technology, Raipur-492101(Chhattisgarh), India.
Mujahid Abbas
- Department of Mathematics, Lahore University of Management Sciences, 54792-Lahore, Pakistan.
Abstract
Using the setting of TVS-valued ordered cone metric spaces ( order is induced by a non normal cone),
common fixed point results for four mappings satisfying implicit contractive conditions are obtained. These
results extend, unify and generalize several well known comparable results in the literature.
Share and Cite
ISRP Style
Hemant Kumar Nashine, Mujahid Abbas, Common fixed point of mappings satisfying implicit contractive conditions in TVS-valued ordered cone metric spaces, Journal of Nonlinear Sciences and Applications, 6 (2013), no. 3, 205--215
AMA Style
Nashine Hemant Kumar, Abbas Mujahid, Common fixed point of mappings satisfying implicit contractive conditions in TVS-valued ordered cone metric spaces. J. Nonlinear Sci. Appl. (2013); 6(3):205--215
Chicago/Turabian Style
Nashine, Hemant Kumar, Abbas, Mujahid. "Common fixed point of mappings satisfying implicit contractive conditions in TVS-valued ordered cone metric spaces." Journal of Nonlinear Sciences and Applications, 6, no. 3 (2013): 205--215
Keywords
- Implicit contraction
- fixed point
- coincidence point
- common fixed point
- weakly compatible mappings
- metric space
- dominating maps
- dominated maps
- ordered metric space
MSC
References
-
[1]
M. Abbas, G. Jungck, Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl. , 341 (2008), 416-420.
-
[2]
M. Abbas, Y.J. Cho, T. Nazir, Common fixed point theorems for four mappings in TVS-valued cone metric spaces, J. Math. Inequalities, 5:2 (2011), 287-299.
-
[3]
M. Abbas, T. Nazir, S. Radenović , Common fixed point of four maps in partially ordered metric spaces, Appl. Math. Lett. , doi:10.1016/j.aml.2011.03.038. (2011)
-
[4]
M. Abbas, B. E. Rhoades, Fixed and periodic point results in cone metric spaces, Appl. Math. Lett. , 22 (2009), 511-515.
-
[5]
R. P. Agarwal , Contraction, approximate contraction with an application to multi-point boundary value problems, J. Comput. Appl. Appl. Math., 9 (1983), 315-325.
-
[6]
R. P. Agarwal, M. A. El-Gebeily, D. O'Regan, Generalized contractions in partially ordered metric spaces, Applicable Anal., 87 (2008), 109-116.
-
[7]
I. Altun, H. Simsek , Some fixed point theorems on ordered metric spaces and application, Fixed Point Theory Appl., 2010 (2010), 17
-
[8]
H. Aydi, Some fixed point results in ordered partial metric spaces, J. Nonlinear Sci. Appl., 4:3 (2011), 210-217.
-
[9]
I. Beg, A. R. Butt , Fixed point for set-valued mappings satisfying an implicit relation in partially ordered metric spaces, Nonlinear Analysis, 71 (2009), 3699-3704.
-
[10]
B. S. Choudhury, A. Kundu, On coupled generalised Banach and Kannan type contractions, J. Nonlinear Sci. Appl., 5 (2012), 259-270.
-
[11]
Lj. B. Ćirić, N. Cakić, M. Rajović, J. S. Ume, Monotone generalized nonlinear contractions in partially ordered metric spaces, Fixed Point Theory and Appl. , 2008 (2008), 11
-
[12]
M. Dordevic, D. Doric, Z. Kadelburg, S. Radenovic, D. Spasic, Fixed point results under c-distance in tvs-cone metric spaces, Fixed Point Theory Appl., 2011 (2011), 29
-
[13]
W. S. Du, A note on cone metric fixed point theory and its equivalence, Nonlinear Anal., 72 (2010), 2259-2261.
-
[14]
L. G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. , 332 (2007), 1468-1476.
-
[15]
D. Ilić, V. Rakoèević, Common fixed points for maps on cone metric space, J. Math. Anal. Appl., 341 (2008), 876-882.
-
[16]
S. Janković, Z. Golubović, S. Radenović, Compatible and weakly compatible mappings in cone metric spaces, Math. Comput. Modelling, doi:10.1016/j.mcm.2010.06.043. (2010)
-
[17]
S. Janković, Z. Kadelburg, S. Radenović, B. E. Rhoades, Assad-Kirk-Type Fixed Point Theorems for a Pair of Nonself Mappings on Cone Metric Spaces , Fixed Point Theory Appl. Article ID 761086, doi:10.1155/2009/761086., 2009 (2009), 16 pages
-
[18]
R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc., 60 (1968), 71-76.
-
[19]
E. M. Mukhamadiev, V. J. Stetsenko, Fixed point principle in generalized metric space, Izvestija AN Tadzh. SSR, fiz.-mat. igeol.-chem. nauki. (in Russian)., 10:4 (1969), 8-19
-
[20]
H. K. Nashine, Coupled common fixed point results in ordered G-metric spaces, J. Nonlinear Sci. Appl., 1 (2012), 1-13.
-
[21]
H. K. Nashine, I. Altun , Fixed point theorems for generalized weakly contractive condition in ordered metric spaces, Fixed Point Theory Appl., 2011 (2011), 20
-
[22]
H. K. Nashine, I. Altun, A common fixed point theorem on ordered metric spaces, Bull. Iranian Math. Soc., (2011), accepted
-
[23]
H. K. Nashine, B. Samet, Fixed point results for mappings satisfying ( \(\psi,\varphi\))-weakly contractive condition in partially ordered metric spaces , Nonlinear Anal. , 74 (2011), 2201-2209.
-
[24]
H. K. Nashine, B. Samet, C. Vetro, Monotone generalized nonlinear contractions and fixed point theorems in ordered metric spaces, Math. Comput. Modelling, 54 (2011), 712-720.
-
[25]
H. K. Nashine, B. Samet, C. Vetro, Coupled coincidence points for compatible mappings satisfying mixed monotone property, J. Nonlinear Sci. Appl. , 5 (2012), 104-114.
-
[26]
H. K. Nashine, W. Shatanawi, Coupled common fixed point theorems for pair of commuting mappings in partially ordered complete metric spaces, Comput. Math. Appl. , 62 (2011), 1984-1993.
-
[27]
J. J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordianry differential equations, Order , 22 (2005), 223-239.
-
[28]
J. O. Olaleru, Some generalizations of fixed point theorems in cone metric spaces, Fixed Point Theory Appl., 2009 (2009), 10
-
[29]
A. I. Perov, The Cauchy problem for systems of ordinary differential equations, in: Approximate Methods of Solving Differential Equations, Kiev, Naukova Dumka, (in Russian), (1964), 115-134
-
[30]
A. I. Perov, A. V. Kibenko, An approach to studying boundary value problems, Izvestija AN SSSR, Ser. Math. (in Russian). , 30:2 (1966), 249-264
-
[31]
A. C. M. Ran, M. C. B. Reurings, A fixed point thm in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 132 (2004), 1435-1443.
-
[32]
D. O'regan, A. Petrutel , Fixed point theorems for generalized contractions in ordered metric spaces, J. Math. Anal. Appl., 341:2 (2008), 241-1252.
-
[33]
Sh. Rezapour, R. Hamlbarani , Some notes on the paper: cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 345 (2008), 719-724.
-
[34]
B. Samet , Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces, Nonlinear Anal., 72 (2010), 4508-4517.
-
[35]
B. Samet, Common fixed point theorems involving two pairs of weakly compatible mappings in K-metric spaces, Applied Mathematics Letters, 24 (2011), 1245-1250.
-
[36]
W. Shatanawi, Partially ordered cone metric spaces and coupled fixed point results, Computers Math. Appl., 60 (2010), 2508-2515.
-
[37]
W. Shatanawi , Some fixed point theorems in ordered G-metric spaces and applications, Abstract and Applied Analysis, 2011 (2011), 11
-
[38]
W. Shatanawi , Some coincidence point results in cone metric spaces, Math. Comput. Mod., 55 (2012), 2023-2028.
-
[39]
W. Shatanawi , On w-compatible mappings and common coupled coincidence point in cone metric spaces , Applied Mathematics Letters, 25 (2012), 925-931.
-
[40]
W. Shatanawi, H. K. Nashine, A generalization of Banach's contraction principle for nonlinear contraction in a partial metric space, J. Nonlinear Sci. Appl., 3 (2012), 139-144.
-
[41]
J. S. Vandergraft, Newton's method for convex opertaors in partially ordered spaces, SIAM J. Numer. Anal., 4 (1967), 406-432.
-
[42]
P. P. Zabrejko, K-normed linear spaces, K-metric, Survey Collect. Math., 48:4-6 (1997), 825-859.