Abstract
The aim of this article is to establish the existence of Common Best Proximity Point (CBPP) for two non-self-mappings on a closed subsets of a metric space having weak \(\mathcal {P}\)-property. Further, we established the same for Kannan and Chatterjea type non-self-contractive mappings with \(k=1\) satisfying demicompact property on a convex bounded closed subset of a Banach space having weak \(\mathcal {P}\)-property. We also present an example to strengthen our main result.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Eldred, A.A., Kirk, W.A., Veeraamani, P.: Proximal normal structure and relatively non expansive mappings. Stud. Math. 171, 283–293 (2005)
Eldred, A.A., Veeraamani, P.: Existence and convergence of best proximity points. J. Math. Anal. Appl. 323, 1001–1006 (2006)
Karapinar, E.: On best proximity point of -Geraghty contractions. Fixed Point Theory Appl. 200 (2013)
Prolla, J.B.: Fixed point theorems for set valued mappings and existence of best approximations. Numer. Funct. Anal. Optim. 5, 449–455 (1983)
Reich, S.: Approximate selections, best proximations, fixed points and invariant sets. J. Math. Anal. Appl. 62, 104–113 (1978)
Sehgal, V.M., Singh, S.P.: A generalization to multifunctions of Fans best approximations theorem. Proc. Am. Math. Soc. 102, 534–537 (1988)
Sehgal, V.M., Singh, S.P.: A theorem on best approximations. Numer. Funct. Anal. Optim. 10, 181–184 (1989)
Dey, L.K., Mondal, S.: Some common best proximity point theorems in a complete metric space. Afr. Mat. (2016). https://doi.org/10.1007/s13370-016-0432-1
Amini-Harandi, A.: Common best proximity points theorems in metric spaces. Optim. Lett. 8, 581–589 (2014). https://doi.org/10.1007/s11590-012-0600-7
Mongkolkeha, C., Kumam, P.: Some common best proximity points for proximity commuting mappings. Optim. Lett. 7(8), 1825–1836 (2013)
Mongkolkeha, C., Kumam, P.: Common best proximity points for proximity commuting mapping with Geraghtys functions. Carpath. J. Math. 31(3), 359–364 (2015)
Basha Sadiq, S., Shahzad, N., Jeyaraj, R.: Common best proximity points, global optimization of multiobjective functions. Appl. Math. Lett. 24(6), 883–886 (2011)
Sen, M.D., Agarwal, R.P.: Common fixed points and best proximity points of two cyclic self-mappings. Fixed Point Theory Appl. 136 (2012)
Zhang, J., Su, Y., Cheng, Q.: A note on A best proximity point theorem for Geraghty-contractions. Fixed Point Theory Appl. 99 (2013)
Petryshyn, W., V.: Construction of fixed points of demicompact mappings in Hilbert space. J. Math. Anal. Appl. 14, 276–284 (1966)
Caballero, J., Harjani, J., Sadarangani, K.: A best proximity point theorem for Geraghty-contractions. Fixed Point Theory Appl. 231 (2012)
Dey, L.K., Mondal, S.: Best proximity point of F-contraction in a complete metric space. Bull. Allahabad Math. Soc. 30(2), 173–189 (2015)
Kannan, R.: Some results on fixed points—II. Am. Math. Mon. 76, 405–408 (1969)
Almeida, A., Karapinar, E., Sadarangani, K.: A note on best proximity theorems under weak-property. Abstr. Appl. Anal. 716825 (2014)
Chatterjea, S.K.: Fixed point theorems. C. R. Acad. Bulg. Sci. 25, 727–730 (1972)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Narayanan, M.S., Marudai, M. (2021). Common Best Proximity Points for Some Contractive Type Mappings. In: Balasubramaniam, P., Ratnavelu, K., Rajchakit, G., Nagamani, G. (eds) Mathematical Modelling and Computational Intelligence Techniques. ICMMCIT 2021. Springer Proceedings in Mathematics & Statistics, vol 376. Springer, Singapore. https://doi.org/10.1007/978-981-16-6018-4_5
Download citation
DOI: https://doi.org/10.1007/978-981-16-6018-4_5
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-16-6017-7
Online ISBN: 978-981-16-6018-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)