Remotest points and approximate remotest points in G-metric spaces

Document Type : Research Paper

Authors

Department of Mathematics, Yazd University, Yazd, Iran.

Abstract

The aim of this paper is to define the concepts of remotest points and approximate remotest points in G-metric spaces and obtain some existence results on these concepts. In particular, we define G-remotest points and G-ϵ-approximate remotest points by considering a cyclic map and prove some results in G-metric spaces.

Keywords


[1] M. Ahmadi Baseri, H. Mazaheri, Remotest points and approximate remotest points in metric spaces, Iranian Journal of Science and Technology,Transactions A: Science, (2015) pp.4.
[2] M. Ahmadi Baseri, H. Mazaheri, On farthest points in fuzzy normed spaces, Jordan Journal of Mathematics and Statistics, 12.2 (2019), 103-114
[3] M. Ahmadi Baseri, H. Mazaheri, Remotest points and best proximity points in metric spaces, Universal Journal of Applied Mathematics, 7(4), (2019), 53-58.
[4] M. Ahmadi Baseri, H. Mazaheri and T. D. Narang, Some results on convergence and existence of best proximity points, Journal of Mahani Mathematical Research Center, 7(1), (2018), 13-24.
[5] M. Baronti, A note on remotal sets in Banach spaces, Publication de L;Institute Math, (53) (1993) 95-98.
[6] M. Baronti, P. L. Papini, Remotal sets revisted, Taiwanese J. Math, (5) (2001) 367-373.
[7] B. S. Choudhury, P. Maity, Best Proximity Point Results in Generalized Metric Spaces. Vietnam Journal of Mathematics, (2014) 1-11.
[8] A. Dehghan Nezhad, H. Mazaheri, New results in G􀀀best approximation in G􀀀metric spaces. Ukrainian Mathematical Journal, 62, (2010) 648-654.
[9] N. Hussain, A. Latif, and P. Salimi, Best Proximity Point Results in G􀀀Metric Spaces, Abstract and Applied Analysis, (2014) (2014).
[10] Z. Mustafa, B. Sims, A new approach to a generalized metric spaces, J. Nonlinear Convex Anal, (7) (2006) 289-297.
[11] M. Sababheh, R. Khalil, Remotality of closed bounded convex sets in re exive spaces, Numer Funct. Anal. Optim, (29) (2006) 1166-1170.
[12] V. Zizler, On some extremal problems in Banach spaces, Math. Scand, (32) (1973) 214-224.
  • Receive Date: 14 September 2020
  • Revise Date: 29 March 2022
  • Accept Date: 14 April 2022
  • First Publish Date: 15 April 2022