On \(\nabla^{**}\)distance and fixed point theorems in generalized partially ordered \(D^*\)metric spaces

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Authors
Alaa Mahmood AL. Jumaili
 School of Mathematics and Statistics, Huazhong University of Science and Technology Wuhan city, Hubei province, Post. No. 430074, China.
Xiao Song Yang
 School of Mathematics and Statistics, Huazhong University of Science and Technology Wuhan city, Hubei province, Post. No. 430074, China.
Abstract
In this paper, we introduce a new concept on a complete generalized \(D^*\)metric space by using the concept
of generalized \(D^*\)metric space (\(D^*\)cone metric space) called \(\nabla^{**}\)distance and, by using the concept of the
\(\nabla^{**}\)distance we prove some new fixed point theorems in complete partially ordered generalized \(D^*\)metric
space which is the main result of our paper.
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ISRP Style
Alaa Mahmood AL. Jumaili, Xiao Song Yang, On \(\nabla^{**}\)distance and fixed point theorems in generalized partially ordered \(D^*\)metric spaces, Journal of Nonlinear Sciences and Applications, 8 (2015), no. 1, 4654
AMA Style
Jumaili Alaa Mahmood AL., Yang Xiao Song, On \(\nabla^{**}\)distance and fixed point theorems in generalized partially ordered \(D^*\)metric spaces. J. Nonlinear Sci. Appl. (2015); 8(1):4654
Chicago/Turabian Style
Jumaili, Alaa Mahmood AL., Yang, Xiao Song. "On \(\nabla^{**}\)distance and fixed point theorems in generalized partially ordered \(D^*\)metric spaces." Journal of Nonlinear Sciences and Applications, 8, no. 1 (2015): 4654
Keywords
 Fixed point theorem
 generalized \(D^*\)metric spaces
 \(\nabla^{**}\)distance.
MSC
References

[1]
R. P. Agarwal, M. A. ElGebeily, D. O'Regan, Generalized contractions in partially ordered metric spaces , Appl. Anal., 87 (2008), 18.

[2]
C. T. Aage, J. N. Salunke, Some fixed points theorems in generalized \(D^*\)metric spaces, Appl. Sci., 12 (2010), 113.

[3]
A. M. AL. Jumaili, X. S. Yang, Fixed point theorems and \(\nabla^{**}\)distance in partially ordered \(D^*\)metric spaces, Int. J. Math. Anal., 6 (2012), 29492955.

[4]
L. B. Ćirić, A generalization of Banach's contraction principle, Proc. Amer. Math. Soc., 45 (1974), 267273.

[5]
L. B. Ćirić, Coincidence and fixed points for maps on topological spaces, Topology Appl., 154 (2007), 31003106.

[6]
L. B. Ćirić, S. N. Jesić, M. M. Milovanović, J. S. Ume, On the steepest descent approximation method for the zeros of generalized accretive operators , Nonlinear Anal.TMA., 69 (2008), 763769.

[7]
B. C. Dhage, Generalized metric spaces and mappings with fixed point, Bull. Calcutta Math, Soc., 84 (1992), 329336.

[8]
J. X. Fang, Y. Gao , Common fixed point theorems under strict contractive conditions in Menger spaces, Nonlinear Anal.TMA., 70 (2009), 184193.

[9]
T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal.TMA., 65 (2006), 13791393.

[10]
T. Gnana Bhaskar, V. Lakshmikantham, J. Vasundhara Devi, Monotone iterative technique for functional differential equations with retardation and anticipation, Nonlinear Anal.TMA., 66 (2007), 22372242.

[11]
N. Hussain, Common fixed points in best approximation for Banach operator pairs with Ćirić type Icontractions, J. Math. Anal. Appl., 338 (2008), 13511363.

[12]
J. J. Nieto, R. R. Lopez, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22 (2005), 223239.

[13]
V. L. Nguyen, X. T. Nguyen, Common fixed point theorem in compact \(D^*\)metric spaces, Int. Math. Forum, 6 (2011), 605612.

[14]
J. J. Nieto, R. R. Lopez, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. Eng. Ser., 23 (2007), 22052212.

[15]
D. O'Regan, R. Saadati , Nonlinear contraction theorems in probabilistic spaces, Appl. Math. Comput., 195 (2008), 8693.

[16]
A. Petruşel, I. A. Rus, Fixed point theorems in ordered Lspaces, Proc. Amer. Math. Soc., 134 (2006), 411418.

[17]
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.

[18]
S. Sedghi, N. Shobe, H. Zhou, A common fixed point theorem in \(D^*\)metric spaces, Fixed Point Theory and Applications. Article ID 27906, (2007), 13 pages.

[19]
R. Saadati, S. M. Vaezpour, P. Vetro, B. E. Rhoades, Fixed point theorems in generalized partially ordered Gmetric spaces, Mathematical and Computer Modelling, 52 (2010), 797801.

[20]
T. Veerapandi, A. M. Pillai, Some common fixed point theorems in \(D^*\) metric spaces , African J. Math. Computer Sci. Research, 4 (2011), 357367.

[21]
T. Veerapandi, A. M. Pillai, A common fixed point theorems in \(D^*\) metric spaces, African J. Math. Computer Sci. Research, 4 (8) (2011), 273280.