Remotest points and approximate remotest points in \(G\)-metric spaces. (English) Zbl 1524.46105
Summary: 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 \(G\)-\(\epsilon\)-approximate remotest points by considering a cyclic map and prove some results in \(G\)-metric spaces.
MSC:
| 46N10 | Applications of functional analysis in optimization, convex analysis, mathematical programming, economics |
| 41A65 | Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) |
| 41A52 | Uniqueness of best approximation |
Keywords:
\(G\)-remotest points; \(G\)-\(\epsilon\)-approximate remotest points; cyclic maps; \(G\)-metric spacesReferences:
| [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 · Zbl 1463.46102 |
| [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. · Zbl 1408.41027 |
| [5] | M. Baronti, A note on remotal sets in Banach spaces, Publication de L , Institute Math, (53) (1993) 95-98. · Zbl 0809.46012 |
| [6] | M. Baronti, P. L. Papini, Remotal sets revisted, Taiwanese J. Math, (5) (2001) 367-373. · Zbl 1030.46018 |
| [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. · Zbl 1224.41095 |
| [9] | N. Hussain, A. Latif, and P. Salimi, Best Proximity Point Results in G−Metric Spaces, Abstract and Applied Analysis, (2014) (2014). · Zbl 1474.54168 |
| [10] | Z. Mustafa, B. Sims, A new approach to a generalized metric spaces, J. Nonlinear Convex Anal, (7) (2006) 289-297. · Zbl 1111.54025 |
| [11] | M. Sababheh, R. Khalil, Remotality of closed bounded convex sets in reflexive spaces, Numer Funct. Anal. Optim, (29) (2006) 1166-1170. · Zbl 1166.46006 |
| [12] | V. Zizler, On some extremal problems in Banach spaces, Math. Scand, (32) (1973) 214-224. · Zbl 0269.46014 |
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