### Coupled Best Proximity Point Theorem for Generalized Contractions in Partially Ordered Metric Spaces

#### Abstract

#### Keywords

#### Full Text:

PDF#### References

A. Abkar and M. Gabeleh, Global optimal solutions of noncyclic mappings in metric spaces, J. Optim. Theory Appl. 153 (2012), 298 – 305.

Ya.I. Alber and S. Guerre-Delabriere, Principle of weakly contractive maps in Hilbert spaces, New Results in Operator Theory and its Applications 98 (1997), 7 – 22.

J. Caballero, J. Harjani and K. Sadarangni, A best proximity point theorem for Geraghtycontractions, Fixed Point Theory Appl. (2012), doi:10.1186/1687-1812-2012-231.

P.N. Dutta and B.S. Choudhury, A generalization of contraction principle in metric spaces, Fixed Point Theory and Applications, 2008, article ID406368, 8 pages.

M. Geraghty, On contractive mappings, Proc. Am. Math. Soc. 40 (1973), 604 – 608.

T. Gnana Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006), 1379 – 1393.

A. Harandi and H.A. Emami, A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations, Nonlinear Anal. 72 (2010), 2238 – 2242.

J. Harjani and K. Sadarangni, Fixed point theorems for weakly contraction mappings in partially ordered sets, Nonlinear Anal. 71 (2009), 3403 – 3410.

J. Harjani and K. Sadarangni, Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Anal. 72 (2010), 1188 – 1197.

M.S. Khan, M. Swaleh and S. Sessa, Fixed point theorems by altering distances between the points, Bull. Aust. Math. Soc. 30 (1) (1984), 1 – 9.

J. Kim and S. Chandok, Coupled common fixed oint theorems for nonlinear contractions mappings without the mixed mononton property in partially ordered spaces, Fixed Theory and Applcations 2013 (2013), 307.

W.A. Kirk, S. Reich and P. Veeramani, Proximinal retracts and best proximity pair theorems, Numer. Funct. Anal. Optim. 24 (2003), 851 – 862.

P. Kumam, V. Pragadeeswarar, M. Marudai and K. Sitthithakerngkiek, Coupled best proximity points in ordered metric spaces, Fixed Theory and Applcations 2014 (2014), 112.

J.J. Nieto and R.R. Lopez, Contractive mapping theorems in partially ordered sets and application to ordinary differential equations, Order 22 (2005), 223 – 239.

B.E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal. TMA 47 (2001), 2683 – 2693.

V. Sankar Raj, A best proximity point theorems for weakly contractive nonself mappings, Nonlinear Anal. 74 (2011), 4804 – 4808.

W. Sintunavarat and P. Kumam, Coupled best proximity point theorem in metric spaces, Fixed Theory and Applcations 2012 (2012), 93.

W. Sintunavarat, P. Kumam and Y. Chao, Coupled best proximity point theorems for nonlinear contractions without mixed monontone property, Fixed Theory and Applcations 2012 (2012), 170.

W. Sintunavarat, Y. Chao and P. Kumam, Coupled fixed point theorems for contraction mapping induced by cone ball-metric in partially ordered spaces without mixed, Fixed Theory and Applcations 2012 (2012), 128.

F. Yan and Y. Su, A new contraction mapping principle in partially ordered metric spaces and applications to ordinary differential equations, Fixed Point Theory Appl. 2012 (2012), doi:10.1186/1687-1812-2012-152.

J. Zhang, Y. Su and Q. Cheng, Best proximity point theorems for generalized contractions in partially ordered metric spaces, Fixed Point Theory Appl. 2013 (2013), 83.

### Refbacks

- There are currently no refbacks.

eISSN 0975-8607; pISSN 0976-5905