Best Proximity Point for Presic Type Mappings on Metric Spaces

Author

Department of Mathematics, Abarkouh Branch, Islamic Azad University, Abarkouh, Iran

Abstract

In this paper, we define the best proximity point for Preˇ si´ c type non-self mappings and prove some best
proximity point theorems in complete metric spaces. c

Keywords


[1] L. B. Ciric, S. B. Presic, On Presic type generalization of the Banach contraction mapping principle, Acta Math.
Univ. Comenian., 76 (2007), 143–147. 

[2] M. Omidvari, S. M. Vaezpour and R. Saadati, Best proximity point theorems for F-contractive non-self mappings,
Miskolc Math. Notes , 15 (2014), 615–623. 

[3] M. Omidvari, S. M. Vaezpour, R. Saadati, S. J. Lee Best proximity point theorems with Suzuki distances, J.
Inequal. Appl., 2015 (2015), 27–44. 

[4] M. Omidvari, S. M. Vaezpour, A best proximity point theorem in metric spaces with generalized distance, J.
Math. Comput. Sci., 13 (2014), 336–342. 

[5] S. B. Presic, Sur la convergence des suites, Comptes Rendus de lAcad. des Sci. de Paris, 260 (1965), 3828–3830.

[6] S. B. Presic, Sur une classe din´ equations aux diff´ erences finite et sur la convergence de certaines suites, Publ.
Inst. Math., (Beograd), 5 (1965), 75–78. 

[7] J. B. Prolla, Fixed point theorems for set valued mappings and existence of best approximations, Numer. Funct.
Anal. Optim., 5 (1982), 449–455. 

[8] S. Reich, Approximate selections, best approximations, fixed points and invariant sets, J. Math. Anal. Appl., 62
(1978), 104–113. 

[9] S. Sadiq Basha, Best proximity point theorems generalizing the contraction principle, Nonlinear Anal., 74 (2011),
5844–5850. 

[10] S. Sadiq Basha, Best proximity point theorems, J. Approx. Theory, 163 (2011), 1772–1781. 

[11] V. Vetrivel, P. Veeramani and P. Bhattacharyya, Some extensions of Fans best approximation theorem, Numer.
Funct. Anal. Optim. 13 (1992), 397–402. 

[12] J. Zhang, Y. Su, Q. Cheng, A note on ”A best proximity point theorem for Geraghty-contractions”, Fixed Point
Theory Appl., 2013 (2013), 99–102.