Coupled coincidence point theorems for mappings without mixed monotone property under cdistance in cone metric spaces

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Authors
Rakesh Batra
 Department of Mathematics, Hans Raj College, University of Delhi, Delhi110007, India.
Sachin Vashistha
 Department of Mathematics, Hindu College, University of Delhi, Delhi110007, India.
Rajesh Kumar
 Department of Mathematics,Hindu College, University of Delhi, Delhi110007, India.
Abstract
Fixed point theory in the field of partially ordered metric spaces has been an area of attraction since
the appearance of Ran and Reurings theorem and Nieto and RodríguezLópez theorem. One of the most
significant hypotheses of these theorems was the mixed monotone property which has been avoided and
replaced by the notion of invariant set in recent years and many statements have been proved using the
concept of invariant set. In this paper we show that the invariant condition guides us to prove many similar
results to which we were exposed to using the mixed monotone property. We present some examples in
support of applicability of our results.
Share and Cite
ISRP Style
Rakesh Batra, Sachin Vashistha, Rajesh Kumar, Coupled coincidence point theorems for mappings without mixed monotone property under cdistance in cone metric spaces, Journal of Nonlinear Sciences and Applications, 7 (2014), no. 5, 345358
AMA Style
Batra Rakesh, Vashistha Sachin, Kumar Rajesh, Coupled coincidence point theorems for mappings without mixed monotone property under cdistance in cone metric spaces. J. Nonlinear Sci. Appl. (2014); 7(5):345358
Chicago/Turabian Style
Batra, Rakesh, Vashistha, Sachin, Kumar, Rajesh. "Coupled coincidence point theorems for mappings without mixed monotone property under cdistance in cone metric spaces." Journal of Nonlinear Sciences and Applications, 7, no. 5 (2014): 345358
Keywords
 fixed point
 coincidence point
 cone metric space
 cdistance
 (F
 g)invariant set.
MSC
References

[1]
R. Batra, S. Vashistha, Coupled coincidence point theorems for nonlinear contractions under cdistance in cone metric spaces, Ann. Funct. Anal., 4 (2013), 138148.

[2]
R. Batra, S. Vashistha , Coupled coincidence point theorems for nonlinear contractions under (F; g)invariant set in cone metric spaces, J. Nonlinear Sci. Appl., 6 (2013), 8696.

[3]
R. Batra, S. Vashistha , Some coupled coincidence point results under cdistance in cone metric spaces, Eng. Math. Lett., 2 (2013), 90114.

[4]
T. G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications , Nonlinear Anal., 65 (2006), 13791393.

[5]
Y. J. Cho, R. Saadati, S. Wang, Common fixed point theorems on generalized distance in ordered cone metric spaces, Comput. Math. Appl. , 61 (2011), 12541260.

[6]
Y. J. Cho, Z. Kadelburg, R. Saadati, W. Shatanawi , Coupled fixed point theorems under weak contractions , Discrete Dyn. Nat. Soc. Article ID 184534, (2012), 9 pages.

[7]
L. G. Huang, X. Zhang , Cone meric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. , 332 (2007), 14681476.

[8]
Sh. Jain, Sh. Jain, L. B. Jain , On Banach contraction principle in a cone metric space , J.Nonliear Sci. Appl., 5 (2012), 252258.

[9]
O. Kada, T. Suzuki, W. Takahashi , Nonconvex minimization theorems and fixed point theorems in complete metric spaces , Math. Japon., 44 (1996), 381391.

[10]
E. Karapinar, Couple fixed point theorems for nonlinear contractions in cone metric spaces, Comput. Math. Appl., 59 (2010), 36563668.

[11]
V. Lakshmikantham, L. Ćirić, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal., 70 (2009), 43414349.

[12]
H. K. Nashine, B. Samet, C. Vetro , Coupled coincidence points for compatible mappings satisfying mixed monotone property, J. Nonlinear Sci. Appl., 5 (2012), 104114.

[13]
J. J. Nieto, R. RodríguezLópez , Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser. ), 23 (2007), 22052212.

[14]
A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 132 (2004), 14351443.

[15]
K. P. R. Rao, S. Hima Bindu, Md. Mustaq Ali , Coupled fixed point theorems in dcomplete topological spaces, J. Nonlinear Sci. Appl., 5 (2012), 186194.

[16]
B. Samet, C. Vetro , Coupled fixed point, Finvariant set and fixed point of Norder , Ann. Funct. Anal., 1 (2010), 4656.

[17]
W. Shatanawi, E. Karapinar, H. Aydi , Coupled coincidence points in partially ordered cone metric spaces with a cdistance, J. Appl. Math, Article ID 312078, (2012), 15 pages.

[18]
W. Sintunavarat, Y. J. Cho, P. Kumam, Coupled fixed point theorems for weak contraction mappings under Finvariant set, Abstr. Appl. Anal. , (), 15 pages.

[19]
D. Turkoglu, M. Abuloha , Cone metric spaces and fixed point theorems in diametrically contractive mappings, Acta Math. Sin. (Engl. Ser. ), 26 (2010), 489496.