Some Approximation in Cone Metric Space and Variational Iterative Method

ABSTRACT

In this paper, we give some new results of common fixed point theorems and coincidence point case for some iterative method. By using of variation iteration method and an effective modification of He’s variation iteration method discusses some integral and differential equations, we give out some new conclusion and more new examples.

In this paper, we give some new results of common fixed point theorems and coincidence point case for some iterative method. By using of variation iteration method and an effective modification of He’s variation iteration method discusses some integral and differential equations, we give out some new conclusion and more new examples.

Cite this paper

N. Chen and J. Chen, "Some Approximation in Cone Metric Space and Variational Iterative Method,"*Applied Mathematics*, Vol. 3 No. 12, 2012, pp. 2007-2018. doi: 10.4236/am.2012.312276.

N. Chen and J. Chen, "Some Approximation in Cone Metric Space and Variational Iterative Method,"

References

[1] D. J. Guo and V. Lakshmikantham, “Nonlinear Problems in Abstract Cones,” Academic Press, Inc., Boston, New York, 1988.

[2] L. G. Hung and X. Zhang, “Cone Metric Spaces and Fixed Point Theorems of Contractive Mappings,” Journal of Mathematical Analysis and Applications, Vol. 332, No. 2, 2007, pp. 1468-1476. doi:10.1016/j.jmaa.2005.03.087

[3] X. Zhang, “Common Fixed Point Theorem of Lipschitz Type Mappings on Cone Metric Space,” Acta Mathematica Sinica, Chinese Series, Vol. 53, No. 6, 2010, pp. 1139-1148.

[4] H. Avdi, H. K. Nashine, B. Samet and H. Yazidi, “Coincidence and Common Fixed Point Results in Partial Ordered Cone Metric Spaces and Applications to Integral Equations,” Nonlinear Analysis, Vol. 74, No. 17, 2011, pp. 6814-6825. doi:10.1016/j.na.2011.07.006

[5] S. H. Cho and M. S. Kim, “Fixed Point Theorems for General Contractive Multi-Valued Mappings,” Applied Mathematics Information, Vol. 27, No. 1-2, 2009, pp. 343-350.

[6] N. Chen and J. Q. Chen, “New Fixed Point Theorems for 1-Set-Contractive Operators in Banach Spaces,” Journal of Fixed Point Theory and Applications, Vol. 6, No. 3, 2011, pp. 147-162.

[7] N. Chen and J. Q. Chen, “Operator Equation and Application of Variational Iterative Method,” Applied Mathematics, Vol. 3, No. 8, 2012, pp. 857-863. doi:10.4236/am.2012.38127

[8] A. Ghorbani and J. Sabaeri-Nadjafi, “An Effective Modification of He’s Variational Iteration Method,” Nonlinear Analysis: Real World Applications, Vol. 10, No. 5, 2009, pp. 2828-2833. doi:10.1016/j.nonrwa.2008.08.008

[9] S. Q. Wang and J. H. He, “Variational Iterative Method for Solving Integral-Differential Equations,” Physics Letters A, Vol. 367, No. 3, 2007, pp. 188-191. doi:10.1016/j.physleta.2007.02.049

[10] N. Chen, B. D. Tian and J. Q. Chen, “Some Random Fixed Point Theorems and Random Altman Type Inequality,” International Journal of Information and Systems Sciences, Vol. 7, No. 1, 2011, pp. 83-91.

[11] S. Jain and V. H. Badshah, “Fixed Point Theorem of Multi-Valued Mappings in Cone Metric Spaces,” International Journal of Mathematical Archive, Vol. 2, No. 12, 2011, pp. 2753-2756.

[12] J. Biazar and H. Aminikahah, “Exact and Numerical Solutions for Non-Linear Burgers’s Equation by VIM,” Mathematical and Computer Modeling, Vol. 49, No. 7-8, 2009, pp. 1394-1400. doi:10.1016/j.mcm.2008.12.006

[1] D. J. Guo and V. Lakshmikantham, “Nonlinear Problems in Abstract Cones,” Academic Press, Inc., Boston, New York, 1988.

[2] L. G. Hung and X. Zhang, “Cone Metric Spaces and Fixed Point Theorems of Contractive Mappings,” Journal of Mathematical Analysis and Applications, Vol. 332, No. 2, 2007, pp. 1468-1476. doi:10.1016/j.jmaa.2005.03.087

[3] X. Zhang, “Common Fixed Point Theorem of Lipschitz Type Mappings on Cone Metric Space,” Acta Mathematica Sinica, Chinese Series, Vol. 53, No. 6, 2010, pp. 1139-1148.

[4] H. Avdi, H. K. Nashine, B. Samet and H. Yazidi, “Coincidence and Common Fixed Point Results in Partial Ordered Cone Metric Spaces and Applications to Integral Equations,” Nonlinear Analysis, Vol. 74, No. 17, 2011, pp. 6814-6825. doi:10.1016/j.na.2011.07.006

[5] S. H. Cho and M. S. Kim, “Fixed Point Theorems for General Contractive Multi-Valued Mappings,” Applied Mathematics Information, Vol. 27, No. 1-2, 2009, pp. 343-350.

[6] N. Chen and J. Q. Chen, “New Fixed Point Theorems for 1-Set-Contractive Operators in Banach Spaces,” Journal of Fixed Point Theory and Applications, Vol. 6, No. 3, 2011, pp. 147-162.

[7] N. Chen and J. Q. Chen, “Operator Equation and Application of Variational Iterative Method,” Applied Mathematics, Vol. 3, No. 8, 2012, pp. 857-863. doi:10.4236/am.2012.38127

[8] A. Ghorbani and J. Sabaeri-Nadjafi, “An Effective Modification of He’s Variational Iteration Method,” Nonlinear Analysis: Real World Applications, Vol. 10, No. 5, 2009, pp. 2828-2833. doi:10.1016/j.nonrwa.2008.08.008

[9] S. Q. Wang and J. H. He, “Variational Iterative Method for Solving Integral-Differential Equations,” Physics Letters A, Vol. 367, No. 3, 2007, pp. 188-191. doi:10.1016/j.physleta.2007.02.049

[10] N. Chen, B. D. Tian and J. Q. Chen, “Some Random Fixed Point Theorems and Random Altman Type Inequality,” International Journal of Information and Systems Sciences, Vol. 7, No. 1, 2011, pp. 83-91.

[11] S. Jain and V. H. Badshah, “Fixed Point Theorem of Multi-Valued Mappings in Cone Metric Spaces,” International Journal of Mathematical Archive, Vol. 2, No. 12, 2011, pp. 2753-2756.

[12] J. Biazar and H. Aminikahah, “Exact and Numerical Solutions for Non-Linear Burgers’s Equation by VIM,” Mathematical and Computer Modeling, Vol. 49, No. 7-8, 2009, pp. 1394-1400. doi:10.1016/j.mcm.2008.12.006