On best proximity points for various \(\alpha\)-proximal contractions on metric-like spaces
Authors
Hassen Aydi
- University of Dammam, Department of Mathematics, College of Education of Jubail, P. O. 12020, Industrial Jubail 31961, Saudi Arabia.
Abdelbasset Felhi
- King Faisal University, Department of Mathematics, College of Sciences, Al-Hassa, Saudi Arabia.
Abstract
We establish some best proximity points for various \(\alpha\)-proximal contractive non-self-mappings in the class
of metric-like spaces. We provide concrete examples. We also present some best proximity point theorems in
metric (metric-like) spaces endowed with a graph and in partially ordered metric spaces.
Keywords
- Metric-like
- best proximity point
- fixed point
- controlled proximal contraction.
References
[1] A. Amini-Harandi, Metric-like spaces, partial metric spaces and fixed points, Fixed Point Theory Appl., 2012 (2012), 10 pages.
[2] H. Aydi, A. Felhi, E. Karapinar, S. Sahmim, Hausdorff metric-like, generalized Nadler's fixed point theorem on metric-like spaces and application, Micolc Math. Notes, (In press).
[3] H. Aydi, A. Felhi, S. Sahmim, Fixed points of multivalued nonself almost contractions in metric-like spaces, Math. Sci. (Springer), 9 (2015), 103-108.
[4] H. Aydi, E. Karapinar, Fixed point results for generalized \(\alpha-\psi\)-contractions in metric-like spaces and applications, Electron. J. Differential Equations, 2015 (2015), 15 pages.
[5] C. Chen, J. Dong, C. Zhu, Some fixed point theorems in b-metric-like spaces, Fixed Point Theory Appl., 2015 (2015), 10 pages.
[6] M. Cvetković, E. Karapınar, V. Rakocević, Some fixed point results on quasi-b-metric-like spaces, J. Inequal. Appl., 2015 (2015), 17 pages.
[7] A. Felhi, H. Aydi, Best proximity points and stability results for controlled proximal contractive set valued mappings, Fixed Point Theory Appl., 2016 (2016), 23 pages.
[8] M. Jleli, E. Karapınar, B. Samet, Best proximity points for generalized \(\alpha-\psi\)-proximal contractive type mappings, J. Appl. Math., 2013 (2013), 10 pages.
[9] S. Karpagam, S. Agrawal, Best proximity point theorems for cyclic orbital Meir-Keeler contraction maps, Non- linear Anal., 74 (2011), 1040-1046.
[10] W. K. Kim, S. Kum, K. H. Lee, On general best proximity pairs and equilibrium pairs in free abstract economies, Nonlinear Anal., 68 (2008), 2216-2227.
[11] W. A. Kirk, S. Reich, P. Veeramani, Proximinal retracts and best proximity pair theorems, Numer. Funct. Anal. Optim., 24 (2003), 851-862.
[12] C. Mongkolkeha, P. Kumam, Best proximity point theorems for generalized cyclic contractions in ordered metric spaces, J. Optim. Theory Appl., 155 (2012), 215-226.
[13] H. K. Nashine, P. Kumam, C. Vetro, Best proximity point theorems for rational proximal contractions, Fixed Point Theory Appl., 2013 (2013), 11 pages.
[14] V. S. Raj, P. Veeramani, best proximity point theorem for weakly contractive non-self-mappings, Nonlinear Anal., 74 (2011), 4804-4808.
[15] S. Sadiq Basha, P. Veeramani, Best proximity pairs and best approximations, Acta Sci. Math. (Szeged), 63 (1997), 289-300.
[16] S. Sadiq Basha, P. Veeramani, Best proximity pair theorems for multifunctions with open fibres, J. Approx. Theory, 103 (2000), 119-129.
[17] B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha\psi\)-contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165.
[18] J. Zhang, Y. Su, Q. Cheng, A note on 'A best proximity point theorem for Geraghty-contractions', Fixed Point Theory Appl., 2013 (2013), 4 pages.