'-BEST PROXIMITY POINT THEOREMS IN METRIC SPACES WITH APPLICATIONS IN PARTIAL METRIC SPACES
In this paper, we introduce the notions of F; '; -proximal contraction and F; '; -weak proximal contraction for non-self mappings and utilize the same to prove some existence and uniqueness of '-best proximity point for such mappings. Some illustrative examples are also given to exhibit the utility of our results. As an application of the concept of '-best proximity point, we deduce some best proximity point theorems in the context of partial metric spaces.
Keywords:
F, ', -proximal contraction, F, ' -weak proximal contraction, '-best proximity point, partial metric space.,
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- M. Al-Thagafi and N. Shahzad, “Convergence and existence results for best proximity points,” Non- linear Analysis: Theory, Methods & Applications, vol. 70, no. 10, pp. 3665–3671, 2009.
- A. A. Eldred and P. Veeramani, “Existence and convergence of best proximity points,” Journal of Mathematical Analysis and Applications, vol. 323, no. 2, pp. 1001–1006, 2006.
- M. Haddadi, “Existence and convergence theorems for best proximity points,” Asian-European Journal of Mathematics, p. 1850005, 2017.
- S. S. Basha, “Best proximity point theorems,” Journal of Approximation Theory, vol. 163, no. 11, pp. 1772–1781, 2011.
- C. Di Bari, T. Suzuki, and C. Vetro, “Best proximity points for cyclic meir–keeler contractions,” Nonlinear Analysis: Theory, Methods & Applications, vol. 69, no. 11, pp. 3790–3794, 2008.
- S. Karpagam and S. Agrawal, “Best proximity point theorems for p-cyclic meir-keeler contractions,” Fixed Point Theory and Applications, vol. 2009, no. 1, p. 197308, 2009.
- A. Abkar and M. Gabeleh, “Global optimal solutions of noncyclic mappings in metric spaces,” Journal of Optimization Theory and Applications, vol. 153, no. 2, pp. 298–305, 2012.
- H. I¸sık, M. S. Sezen, and C. Vetro, “ϕ-best proximity point theorems and applications to variational inequality problems,” Journal of Fixed Point Theory and Applications, pp. 1–13, 2017.
- M. Jleli, B. Samet, and C. Vetro, “Fixed point theory in partial metric spaces via ϕ-fixed points concept in metric spaces,” Journal of Inequalities and Applications, vol. 2014, no. 1, p. 426, 2014.
- M. Asadi, “Discontinuity of control function in the (f, ϕ, θ)-contraction in metric spaces,” Filomat, vol. 31, no. 17, 2017.
- P. Kumrod and W. Sintunavarat, “A new contractive condition approach to ϕ-fixed point results in metric spaces and its applications,” Journal of Computational and Applied Mathematics, vol. 311, pp. 194–204, 2017.
- S. G. Matthews, “Partial metric topology,” Annals of the New York Academy of Sciences, vol. 728, no. 1, pp. 183–197, 1994.
- A. Nastasi and P. Vetro, “Fixed point results on metric and partial metric spaces via simulation functions,” J. Nonlinear Sci. Appl, vol. 8, no. 6, pp. 1059–1069, 2015.
- ISSN: 2146-1147
- Başlangıç: 2010
- Yayıncı: Turkic World Mathematical Society
Sayıdaki Diğer Makaleler
M. A. NOOR, K. I. NOOR, S. IFTİKHAR
K. DOGAN, F. GURSOY, V. KARAKAYA
T. H. Dizman (ŞİMŞEKLER), N. Demirtaş (TOZLU), Ş. YUKSEL
A. R. HAGHİGHİ, A. AGHAZEDEH, A. ABEDİNİ