Common best proximity points of some graph-theoretical notions of dominating pairs
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Keywords:
best proximity point, common best proximity point, Geraghty’s type contraction, G–proximalAbstract
This article deals with a metric space endowed with a directed graph. In order to obtain common
best proximity point results, we introduce a concept of Geraghty’s type contraction satisfying certain
properties on the graph. An example and some consequences are also provided
References
I. Altun, M. Aslantas, H. Sahin, KW-Type Nonlinear Contractions and Their Best Proximity Points. Numerical Functional Analysis and Optimization, 2021, 42(8), 935–954.
W. Atiponrat, S. Dangskul, A. Khemphet, Coincidence point theorems for KC-contraction mappings in JS-metric spaces endowed with a directed graph. Carpathian Journal of Mathematics, 2019, 35(3), 263–272.
S. Sadiq Basha, Common best proximity points: global minimization of multi-objective functions. J. Glob. Optim., 2012,54, 367–373.
S. Sadiq Basha, N. Shahzad, R. Jeyaraj, Common best proximity points: global optimization of multi-objective functions. Appl. Math. Lett., 2011, 24, 883–886.
S. Sadiq Basha, P. Veeramani, Best proximity pair theorems for multifunctions with open fibres. J. Approx. Theory,2000, 103(1), 119–129.
P. Charoensawan, W. Atiponrat, Common fixed point and coupled coincidence point theorems for Geraghty’s type contraction mapping with two metrics endowed with a directed graph. J. Math. 2017, Art. ID 5746704. https://doi.org/10.1155/2017/5746704
L. Chen, Common best proximity points theorems. JMRA. 2019, 39(3), 289–294.
P. Cholamjiak, Fixed point theorems for Banach type contraction on Tvs-cone metric spaces endowed with a graph. J. Comput. Anal. Appl, 2014, 16, 338–345.
S. Dangskul, R. Suparatulatorn, Global Minimization of Common Best Proximity Points for Generalized Cyclic ϕ-Contractions in Metric Spaces, Thai Journal of Mathematics, 2020, 18(3), 1173–1183.
A. A. Eldred, P. Veeramani, Existence and convergence of best proximity points. J. Math. Anal. Appl., 2006, 323(2), 1001–1006.
K. Fan, Extensions of two fixed point theorems of F.E. Browder. Math. Z., 1969, 122, 234–240.
H. A. Hammad, W. Cholamjiak, D. Yambangwai, H. Dutta, A modified shrinking projection methods for numerical reckoning fixed points of G-nonexpansive mappings in Hilbert spaces with graphs. Miskolc Math. Notes, 2019, 20(2), 941–956.
J. Jachymski, The contraction principle for mappings on a metric space with a graph. Proc. Am. Math. Soc., 2008, 136, 1359–1373.
E. Karapınar, Best proximity points of cyclic mappings. Appl. Math. Lett., 2012, 25, 1761–1766.
E. Karapınar, Best proximity points of Kannan type cyclic weak ϕ-contractions in ordered metric spaces. An. Ştiinţ.Univ. “Ovidius” Constanţa Ser. Mat., 2012, 20(3), 51–63.
E. Karapınar, On best proximity point of ψ-Geraghty contractions. Fixed Point Theory Appl., 2013. https://doi.org/10.1186/1687-1812-2013-200
E. Karapınar, T. Abdeljawad, F. Jarad, Applying new fixed point theorems on fractional and ordinary differential equations. Adv. Difference Equ., 2019. Paper No. 421.
E. Karapınar, I. M. Erhan, Best proximity point on different type contractions. Appl. Math. Inform. Sci., 2011, 3,342–353.
E. Karapınar, F. Khojasteh, An approach to best proximity points results via simulation functions. J. Fixed Point Theory Appl., 2017, 19, 1983–1995. https://doi.org/10.1007/s11784-016-0380-2
E. Karapınar, V. Pragadeeswarar, M. Marudai, Best proximity point for generalized proximal weak contractions in complete metric space. J. Appl. Math., 2014. Article ID 150941.
A. Khemphet, P. Chanthorn, N. Phudolsitthiphat, Common best proximity coincidence point theorem for dominating proximal generalized Geraghty in complete metric spaces. Journal of Function Spaces., 2020. Article ID 9620254. https://doi.org/10.1155/2020/9620254
W. A. Kirk, S. Reich, P. Veeramani, Proximinal retracts and best proximity pair theorems. Numer. Funct. Anal. Optim.,2003, 24(7–8), 851–862.
C. Klanarong, S. Suantai, Best proximity point theorems for G-proximal generalized contraction in complete metric spaces endowed with graphs. Thai J. Math., 2017, 15(1), 261–276.
P. Kumam, C. Mongkolkeha, Common best proximity points for proximity commuting mapping with Geraghty’s functions. Carpath. J. Math., 2015, 31(3), 359–364.
C. Mongkolkeha, Y. J. Cho, P. Kumam, Best proximity points for Geraghty’s proximal contraction mappings. Fixed Point Theory Appl., 2013, 180.
H. Sahin, M. Aslantas, I. Altun, Best proximity and best periodic points for proximal nonunique contractions. Journal of Fixed Point Theory and Applications, 2021, 23(4), 1–14.
S. Suantai, M. Donganont, W. Cholamjiak, Hybrid methods for a countable family of G-nonexpansive mappings in Hilbert spaces endowed with graphs. Mathematics., 2019, 7(10), Article ID 936. https://doi.org/10.3390/math7100936
R. Suparatulatorn, W. Cholamjiak, S. Suantai, A modified S-iteration process for G–nonexpansive mappings in Banach spaces with graphs. Numerical Algorithms., 2018, 77, 479–490.
R. Suparatulatorn, S. Suantai, A new hybrid algorithm for global minimization of best proximity points in Hilbert spaces. Carpathian J. Math., 2019, 35(1), 95–102.
R. Suparatulatorn, S. Suantai, W. Cholamjiak, Hybrid methods for a finite family of G–nonexpansive mappings in Hilbert spaces endowed with graphs. AKCE Int. J. Graphs Comb., 2017, 14(2), 101–111.
