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BEST PROXIMITY POINTS AND FIXED POINTS WITH $R$-FUNCTIONS IN THE FRAMEWORK OF $w$-DISTANCES

Part of: Nonlinear operators and their properties Connections with other structures, applications

Published online by Cambridge University Press:  17 December 2018

ALEKSANDAR KOSTIĆ Open the ORCID record for ALEKSANDAR KOSTIĆ [Opens in a new window] ,
ERDAL KARAPINAR Open the ORCID record for ERDAL KARAPINAR [Opens in a new window]  and
VLADIMIR RAKOČEVIĆ Open the ORCID record for VLADIMIR RAKOČEVIĆ [Opens in a new window]
ALEKSANDAR KOSTIĆ*
Affiliation:
Faculty of Sciences and Mathematics, University of Niš, Niš, Serbia email akos2804@gmail.com
ERDAL KARAPINAR
Affiliation:
Department of Medical Research, China Medical University, Taichung, Taiwan email erdalkarapinar@yahoo.com
VLADIMIR RAKOČEVIĆ
Affiliation:
Faculty of Sciences and Mathematics, University of Niš, Niš, Serbia email vrakoc@sbb.rs
*
✉akos2804@gmail.com
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Abstract

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We study best proximity points in the framework of metric spaces with $w$-distances. The results extend, generalise and unify several well-known fixed point results in the literature.

Keywords

best proximity pointsfixed pointsR-functionsw-distances

MSC classification

Primary: 47H10: Fixed-point theorems
Secondary: 54H25: Fixed-point and coincidence theorems
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 99 , Issue 3 , June 2019 , pp. 497 - 507
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

Footnotes

The first and third author are supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia, Grant No. 174025.

References

Găvruţa, L., Găvruţa, P. and Khojasteh, F., ‘Two classes of Meir–Keeler contractions’, Preprint, 2014, arXiv:1405.5034 [math.FA].Google Scholar
Geraghty, M. A., ‘On contractive mappings’, Proc. Amer. Math. Soc. 40 (1973), 604–608.Google Scholar
Gholizadeh, L. and Karapınar, E., ‘Best proximity point results in dislocated metric spaces via R-functions’, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. 112(4) (2018), 1391–1407.Google Scholar
Jleli, M., Karapinar, E. and Samet, B., ‘Best proximity point results for MK-proximal contractions’, Abstr. Appl. Anal. 2012 (2012), Article ID 193085, 14 pages.Google Scholar
Kada, O., Suzuki, T. and Takahashi, W., ‘Nonconvex minimization theorems and fixed point theorems in complete metric space’, Math. Japonica 44 (1996), 381–391.Google Scholar
Karapınar, E. and Khojasteh, F., ‘An approach to best proximity points results via simulation functions’, J. Fixed Point Theory Appl. 19(3) (2017), 1983–1995.Google Scholar
Khojasteh, F., Shukla, S. and Radenović, S., ‘A new approach to the study of fixed point theorems via simulation functions’, Filomat 29 (2015), 1189–1194.Google Scholar
Kostić, A., Rakočević, V. and Radenović, S., ‘Best proximity points involving simulation functions with w 0 -distance’, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. (to appear), available at https://doi.org/10.1007/s13398-018-0512-1.Google Scholar
Meir, A. and Keeler, E., ‘A theorem on contraction mappings’, J. Math. Anal. Appl. 28 (1969), 326–329.Google Scholar
Nastasi, A., Vetro, A. P. and Radenović, S., ‘Some fixed point results via R-functions’, Fixed Point Theory Appl. 2016 (2016), Article ID 2016:81, 12 pages.Google Scholar
Pirbavafa, S., Vaezpour, S. M. and Khojasteh, F., ‘Global minimization of R-contractions via best proximity points’, J. Math. Anal. 8(3) (2017), 125–134.Google Scholar
Roldán López de Hierro, A. F. and Shahzad, N., ‘New fixed point theorem under R-contractions’, Fixed Point Theory Appl. 2015 (2015), Article ID 2015:98, 18 pages.Google Scholar
Takahashi, W., Wong, N. C. and Yao, J. C., ‘Fixed point theorems for general contractive mappings with w-distances in metric spaces’, J. Nonlinear Convex Anal. 14 (2013), 637–648.Google Scholar
Tchier, F., Vetro, C. and Vetro, F., ‘Best approximation and variational inequality problems involving a simulation function’, Fixed Point Theory Appl. 2016 (2016), Article ID 2016:26, 15 pages.Google Scholar
Zarinfar, F., Khojasteh, F. and Vaezpour, S. M., ‘A new approach to the study of fixed point theorems with w-distances via R-functions’, J. Funct. Spaces 2016 (2016), Article ID 6978439, 9 pages.Google Scholar