### Coupled Best Proximity Points under the Proximally Coupled Contraction in a Complete Ordered Metric Space

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A. Abkar and M. Gabeleh, Best proximity points for cyclic mappings in ordered metric spaces, J. Optim. Theory Appl. 150 (1) (2011), 188–193.

A. Abkar and M. Gabeleh, Generalized cyclic contractions in partially ordered metric spaces, Optim. Lett. 6 (8) (December 2012), 1819–1830.

M.A. Al-Thagafi and N. Shahzad, Convergence and existence results for best proximity points, Nonlinear Anal. 70 (2009), 3665–3671.

A.H. Ansari, Note on “(varphi)-(psi)-contractive type mappings and related fixed point”, The 2nd Regional Conference on Mathematics and Applications, Payame Noor University, 2014, pp. 377–380.

A. Anthony Eldred and P. Veeramani, Existence and convergence of best proximity points, J. Math. Anal. Appl. 323 (2006), 1001–1006.

G.V.R. Babu and P.D. Sailaja, A fixed point theorem of generalized weakly contractive maps in orbitally complete metric spaces, Thai Journal of Mathematics 9 (1) (2011), 1–10.

S. Sadiq Basha, Discrete optimization in partially ordered sets, J. Global Optim. 54 (3) (November 2012), 511–517.

S. Sadiq Basha and P. Veeramani, Best proximity pair theorems for multifunctions with open fibres, J. Approx. Theory. 103 (2000), 119–129.

K. Fan, Extensions of two fixed point theorems of F.E. Browder, Math. Z. 122 (1969), 234–240. [10] T. Gnana Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006), 1379–1393.

N. Hussain, M. Abbas, A. Azam and J. Ahmad, Coupled coincidence point results for a generalized compatible pair with applications, Fixed Point Theory and Applications 2014 (2014), 62.

M. Jleli and B. Samet, Remarks on the paper: Best proximity point theorems: An exploration of a common solution to approximation and optimization problems, Appl. Math. Comp. 228 (2014), 366–370.

E. Karapinar and W. Sintunavarat, The existence of an optimal approximate solution theorems for generalized (alpha)-proximal contraction nonself mappings and applications, Fixed Point Theory and Applications 2013 (2013), 323.

M.S. Khan, M. Swaleh and S. Sessa, Fixed point theorems by altering distances between the points, Bulletin of the Australian Mathematical Society 30 (1) (1984), 1–9.

W.K. Kim and K.H. Lee, Existence of best proximity pairs and equilibrium pairs, J. Math. Anal. Appl. 316 (2) (2006), 433–446.

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, H. Aydi, E. Karapinar and W. Sintunavarat, Best proximity points and extension of Mizoguchi-Takahashi’s fixed point theorems, Fixed Point Theory and Applications 2013 (2013), 242.

P. Kumam, V. Pragadeeswarar, M. Marudai and K. Sitthithakerngkiet, Coupled best proximity points in ordered metric spaces, Fixed Point Theory and Applications 2014 (2014), 107.

M.A. Kutbi, A. Azam, J. Ahmad and C. Di Bari, Some common coupled fixed point results for generalized contraction in complex-valued metric spaces, Journal of Applied Mathematics 2013, Article ID 352927, 10 pages.

V. Lakshmikanthama and L. Ciric, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. 70 (12) (2009), 4341–4349.

Nguyen Van Luong and Nguyen Xuan Thuan, Coupled fixed point theorems for mixed monotone mappings and an application to integral equations, Comput. Math. Appl. 62 (11) (2011), 4238–4248.

Nguyen Van Luong and Nguyen Xuan Thuan, Coupled fixed points in partially ordered metric spaces and application, Nonlinear Anal. 74 (2011), 983–992.

V. Pragadeeswarar and M. Marudai, Best proximity points: approximation and optimization in partially ordered metric spaces, Optim. Lett. 7 (8) (December 2013), 1883–1892.

V. Sankar Raj, A best proximity point theorem for weakly contractive non-self-mappings, Nonlinear Anal. 74 (2011), 4804–4808.

M. De la Sen and R.P. Agarwal, Some fixed point-type results for a class of extended cyclic selfmappings with a more general contractive condition, Fixed Point Theory Appl. 2011, 59, 2011.

P.S. Srinivasan and P. Veeramani, On existence of equilibrium pair for constrained generalized games, Fixed Point Theory Appl. 1 (2004), 21–29.

W. Sintunavarat and P. Kumam, The existence theorems of an optimal approximate solution for generalized proximal contraction mappings, Abstr. Appl. Anal. 2013 (2013), Article ID 375604, 8 pages.

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

W. Shatanawi, Partially ordered metric spaces and coupled fixed point results, Comput. Math. Appl. 60 (2010), 2508–2515.

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