Abstract
The main purpose of this article is to present a partial answer to the question raised by T. Stephen et al. in a recent paper [T. Stephen, Y. Rohen, H. Isik, L. Shanjit, Some best proximity point results for generalized cyclic contraction mappings, Int. J. Nonlinear Anal. Appl., DOI: 10.22075/ijnaa.2023.24597.3033] which is related to the existence of best proximity points for generalized pointwise cyclic contractions without T-restriction property.
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References
Al-Thagafi, M.A., and N. Shahzad. 2009. Convergence and existence results for best proximity points. Nonlinear Anal. 70: 3665–3671.
Eldred, A.A., and P. Veeramani. 2006. Existence and convergence of best proximity points. J. Math. Anal. Appl. 323: 1001–1006.
Eldred, A.A., W.A. Kirk, and P. Veeramani. 2005. Proximal normal structure and relatively nonexpansive mappings. Studia Math. 171: 283–293.
Espínola, R. 2008. A new approach to relatively nonexpansive mappings. Proc. Am. Math. Soc. 136: 1987–1996.
Gabeleh, M., and N. Shahzad. 2016. Best proximity points, cyclic Kannan maps and geodesic metric spaces. J. Fixed Point Theory Appl. 18: 167–188.
Gabeleh, M. 2015. Best proximity points for weak proximal contractions. Bull. Malaysian Math. Sci. Soc. 38: 143–154.
Gabeleh, M., and C. Vetro. 2018. A new extension of Darbzo’s fixed point theorem using relatively Meir-Keeler condensing operators. Bull. Australian Math. Soc. 98: 286–297.
Kosuru, G. S. R., and P. Veeramani. 2011. A Note on Existence and Convergence of Best Proximity Points for Pointwise Cyclic Contractions. Numer. Funct. Anal. Optim. 32: 821–830.
Stephen, T., Y. Rohen, H. Isik, and L. Shanjit. Some best proximity point results for generalized cyclic contraction mappings, Int. J. Nonlinear Anal. Appl., https://doi.org/10.22075/ijnaa.2023.24597.3033(In Press).
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The author would like to thank the anonymous referee for his valuable comments and suggestions.
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Communicated by Simeon Reich.
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Gabeleh, M. On generalized pointwise cyclic contractions without T-restriction property. J Anal (2024). https://doi.org/10.1007/s41478-024-00749-w
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DOI: https://doi.org/10.1007/s41478-024-00749-w