SOME COMMENTS ON BEST PROXIMITY POINTS FOR ORDERED PROXIMAL CONTRACTIONS

Moosa Gabeleh; Jack Markin; Manuel De La Sen

doi:10.11948/20210266

2022 Volume 12 Issue 4

Article Contents

Article navigation > Journal of Applied Analysis & Computation > 2022 > 12(4): 1434-1442

Next Article Previous Article

Moosa Gabeleh, Jack Markin, Manuel De La Sen. SOME COMMENTS ON BEST PROXIMITY POINTS FOR ORDERED PROXIMAL CONTRACTIONS[J]. Journal of Applied Analysis & Computation, 2022, 12(4): 1434-1442. doi: 10.11948/20210266

Citation:

Moosa Gabeleh, Jack Markin, Manuel De La Sen. SOME COMMENTS ON BEST PROXIMITY POINTS FOR ORDERED PROXIMAL CONTRACTIONS[J]. Journal of Applied Analysis & Computation, 2022, 12(4): 1434-1442. doi: 10.11948/20210266

SOME COMMENTS ON BEST PROXIMITY POINTS FOR ORDERED PROXIMAL CONTRACTIONS

1.
Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran
2.
1440 8th St. Golden, Co 80401, USA
3.
Institute of Research and Development of Processes, University of the Basque Country, 48940 Leioa, Bizkaia, Spain

Corresponding author: Email: gab.moo@gmail.com, Gabeleh@abru.ac.ir(M. Gabeleh)
Fund Project: The third author is thankful for the support of Basque Government (No.1207-19)

Abstract

Abstract

In this article, we focus on the existence of an optimal approximate solution, designated as a best proximity point for non-self mappings which are ordered proximal contractions in the setting of partially ordered metric spaces and prove that these results are particular cases of existing fixed point theorems in the literature.
- Best proximity point /
- fixed point /
- proximal contraction /
- integral type contraction
MSC: 54H25, 47H10

FullText(HTML)

References

[1]	G. V. R. Babu, P. D. Sailaja and K. T. Kidane, A fixed point theorem in orbitally complete partially ordered metric spaces, J. Operators, 2013, 2013, 1–8. Google Scholar
[2]	S. Chandok, B. S. Choudhury and N. Metiya, Fixed point results in ordered metric spaces forrational type expressions with auxiliary functions, J. Egyptian Math. Soc., 2015, 23, 95–101. doi: 10.1016/j.joems.2014.02.002 CrossRef Google Scholar
[3]	L. B. Ćirić, A generalization of Banach's contraction principle, Proc. Amer. Math. Soc., 1974, 45, 267–273. Google Scholar
[4]	K. Chairaa, A. Eladraouib and M. Kabilc, Extensions of some fixed point theorems for weak-contraction mappings in partially ordered modular metric spaces, Iranian Journal of Mathematical Sciences and Informatics, 2020, 15, 111–124. doi: 10.29252/ijmsi.15.1.111 CrossRef Google Scholar
[5]	H. Ding, Z. Kadelburg and H. K. Nashine, Common fixed point theorems for weakly increasing mappings on ordered orbitally complete metric spaces, Fixed Point Theory Apll., 2012, 2012, 1–14. doi: 10.1186/1687-1812-2012-1 CrossRef Google Scholar
[6]	K. S. Eke and G. J. Oghonyon, Some fixed point theorems in ordered partial metric spaces with applications, Cogent Mathematics & Statistics, 2018, 5, 1–11. Google Scholar
[7]	K. Fallahi, H. Ghahramani and G. Soleimani Rad, Integral type contractions in partially ordered metric spaces and best proximity point, Iranian J. Sci. Tech., Transactions A: Sci., 2020, 44, 177–183. doi: 10.1007/s40995-019-00807-0 CrossRef Google Scholar
[8]	M. Gabeleh and J. Markin, A note on the paper "Best proximity point results for p -proximal contractions", Acta Math. Hungar., 2021, 164, 326–329. doi: 10.1007/s10474-021-01139-5 CrossRef Google Scholar
[9]	M. Gabeleh and J. Markin, Some notes on the paper "On best proximity points of interpolative proximal contractions", Quaestiones Mathematicae, 2021. DOI: 10.2989/16073606.2021.1951872. CrossRef Google Scholar
[10]	V. Gupta and R. Deep, Some coupled fixed point theorems in partially ordered S-metric spaces, Miskolc Mathematical Notes, 2015, 16, 181–194. doi: 10.18514/MMN.2015.1135 CrossRef Google Scholar
[11]	V. Gupta, G. Jungck and N. Mani, Some novel fixed point theorems in partially ordered metric spaces, AIMS Math., 2020, 5, 4444–4452. doi: 10.3934/math.2020284 CrossRef Google Scholar
[12]	R. Kannan, Some results on fixed points-Ⅱ, Am. Math. Mon., 1969, 76, 405–408. Google Scholar
[13]	N. Mani and J. Jindal, Some new fixed point theorems for generalized weak contraction in partially ordered metric spaces, Computational and Mathematical Methods, 2020, 2(5), 1–9. Google Scholar
[14]	J. J. Nieto and R. Rodriguez-Lopez, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 2005, 22, 223–239. doi: 10.1007/s11083-005-9018-5 CrossRef Google Scholar
[15]	M. A. Olona, T. A. Alakoya, O. E. Owolabi and O. T. Mewomo, Inertial shrinking projection algorithm with self-adaptive step size for split generalized equilibrium and fixed point problems for a countable family of nonexpansive multivalued mappings, Demonstratio Mathematica, 2021, 54, 47–67. doi: 10.1515/dema-2021-0006 CrossRef Google Scholar
[16]	V. Sankar Raj, A best proximity point theorem for weakly contractive non-self-mappings, Nonlinear Anal., 2011, 74, 4804–4808. doi: 10.1016/j.na.2011.04.052 CrossRef Google Scholar
[17]	S. Sadiq Basha, Discrete optimization in partially ordered sets, J. Global Optim., 2012, 54, 511–517. doi: 10.1007/s10898-011-9774-2 CrossRef Google Scholar
[18]	N. Seshagiri Rao, K. Kalyani and K. Khatri, Contractive mapping theorems in Partially ordered metric spaces, CUBO, 2020, 22, 203–214. doi: 10.4067/S0719-06462020000200203 CrossRef Google Scholar
[19]	H. Zegeye and G. Bekele Wega, Approximation of a common f-fixed point of f-pseudocontractive mappings in Banach spaces, Rendiconti del Circolo Matematico di Palermo Series 2 volume, 2021, 70, 1139–1162. doi: 10.1007/s12215-020-00549-8 CrossRef Google Scholar