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International Journal of Nonlinear Analysis and Applications
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Volume Volume 8 (2017)
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Nashine, H., Kadelburg, Z. (2017). Existence of common best proximity points of generalized $S$-proximal contractions. International Journal of Nonlinear Analysis and Applications, 8(2), 1-8. doi: 10.22075/ijnaa.2017.859.1153
Hemant Nashine; Zoran Kadelburg. "Existence of common best proximity points of generalized $S$-proximal contractions". International Journal of Nonlinear Analysis and Applications, 8, 2, 2017, 1-8. doi: 10.22075/ijnaa.2017.859.1153
Nashine, H., Kadelburg, Z. (2017). 'Existence of common best proximity points of generalized $S$-proximal contractions', International Journal of Nonlinear Analysis and Applications, 8(2), pp. 1-8. doi: 10.22075/ijnaa.2017.859.1153
Nashine, H., Kadelburg, Z. Existence of common best proximity points of generalized $S$-proximal contractions. International Journal of Nonlinear Analysis and Applications, 2017; 8(2): 1-8. doi: 10.22075/ijnaa.2017.859.1153

Existence of common best proximity points of generalized $S$-proximal contractions

Article 1, Volume 8, Issue 2, Summer and Autumn 2017, Page 1-8  XML PDF (349 K)
Document Type: Research Paper
DOI: 10.22075/ijnaa.2017.859.1153
Authors
Hemant Nashine 1; Zoran Kadelburg2
1Department of Mathematics, Texas A & M University-Kingsville-78363-8202, Texas, USA
2University of Belgrade, Faculty of Mathematics, Studentski trg 16, 11000 Beograd, Serbia
Abstract
In this article, we introduce a new notion of proximal contraction, named as generalized S-proximal contraction and derive a common best proximity point theorem for proximally commuting non-self mappings, thereby yielding the common optimal approximate solution of some fixed point equations when there is no common solution. We furnish illustrative examples to highlight our results. We extend some results existing in the literature.
Keywords
common best proximity point; optimal approximate solution; proximally commuting mappings
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