Best Proximity Pair Theorems for Multifunctions with Open Fibres
By S. Sadiq Basha, P. Veeramani. 2000
243 citations recorded by the source corpus.
Let A and B be non-empty subsets of a normed linear space, and f:A->B be a single valued function. A solution to the functional equation fx=x, (x@?A) will be an element x"o in A such that fx"o=x"o (i.e., such that d(fx, x)=0). In the case of non-existence of a solution to the equation fx=x, it is natural to explore the existence of an optimal approximate solution that will fulfill the requirement to some extent. In other words, an element x"o in A should be found in such a way that d(x"o, fx"o)=Min{d(x, fx):x@?A}. Thus, the crux of finding an optimal approximate solution to the aforesaid equation fx=x boils down to ascertaining a solution to the optimization problem Min{d(x, fx):x@?A}. But, d(x, fx)>=d(A, B) for all x@?A. So, in the case of seeking an optimal approximate solution to the aforesaid equation fx=x, it should be contemplated to find an element x"o in A such that d(x"o, fx"o)=d(A, B). Indeed, given a multifunction T: A->2^B with open fibres, best proximity pair theorems, furnishing the sufficient conditions for the existence of an element x"o@?A such that d(x"o, Tx"o)=d(A, B), are proved in this paper.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/decb772dc1951337b2827632ab3d83f453313d32
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In Computational Theory and Mathematics
- S. Sadiq Basha
- Naseer Shahzad
- Poom Kumam
- Wutiphol Sintunavarat
- V. Sankar Raj
- P. Veeramani
- Simeon Reich
- Dang Van Hieu
In Geometry and Topology
- Poom Kumam
- Wutiphol Sintunavarat
- S. Sadiq Basha
- Naseer Shahzad
- V. Sankar Raj
- P. Veeramani
- Simeon Reich
- E. Karapınar
In Numerical Analysis
- Naseer Shahzad
- V. Sankar Raj
- S. Sadiq Basha
- P. Veeramani
- Poom Kumam
- Simeon Reich
- Dang Van Hieu
- Duong Viet Thong
Citations in the corpus
- Proximinal Retracts and Best Proximity Pair Theorems (2003, background): “gif"/> is a multifunction defined on suitable subsets A and B of a normed linear space (or a locally convex Hausdorff topological vector space) can be found in Sadiq Basha and Veeramani ( 1997 2000 ), Srinivasan ( 2001 ), and Sadiq Basha et al.”
- Coupled best proximity point theorem in metric Spaces (2012, background): “[42], Eldred and Veramani [11], Mongkolkeha and Kumam [25] and Basha and Veeramani [5, 6, 7, 8] (see also [3, 15, 16, 17, 18, 19, 20, 21] and reference therein.”
- Best proximity point theorems for generalized proximal contractions (2012, background): “Also, best proximity point theorems for various kinds of multi-valued mappings have been accomplished in [21-31].”
- Best proximity pair theorems for relatively nonexpansive mappings (2009, background): “In [8], Sadiq Basha and Veeramani proved the following result.”