Document Details
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Document Type |
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Article In Journal |
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Document Title |
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Common best proximity points: Global optimization of multi- objective functions Common best proximity points: Global optimization of multi- objective functions |
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Subject |
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Mathematics |
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Document Language |
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English |
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Abstract |
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Assume that A and B are non-void subsets of a metric space, and that S:A→B and T:A→B are given non-self-mappings. In light of the fact that S and T are non-self-mappings, it may happen that the equations Sx=x and Tx=x have no common solution, named a common fixed point of the mappings S and T. Subsequently, in the event that there is no common solution of the preceding equations, one speculates about finding an element x that is in close proximity to Sx and Tx in the sense that d(x,Sx) and d(x,Tx) are minimum. Indeed, a common best proximity point theorem investigates the existence of such an optimal approximate solution, named a common best proximity point of the mappings S and T, to the equations Sx=x and Tx=x when there is no common solution. Moreover, it is emphasized that the real valued functions x→d(x,Sx) and x→d(x,Tx) evaluate the degree of the error involved for any common approximate solution of the equations Sx=x and Tx=x. Owing to the fact that the distance between x and Sx, and the distance between x and Tx are at least the distance between A and B for all x in A, a common best proximity point theorem accomplishes the global minimum of both functions x→d(x,Sx) and x→d(x,Tx) by postulating a common approximate solution of the equations Sx=x and Tx=x for meeting the condition that d(x,Sx)=d(x,Tx)=d(A,B). This work is devoted to an interesting common best proximity point theorem for pairs of non-self-mappings satisfying a contraction-like condition, thereby producing common optimal approximate solutions of certain simultaneous fixed point equations. |
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ISSN |
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0893-9659 |
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Journal Name |
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Applied Mathematics Letters |
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Volume |
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24 |
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Issue Number |
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6 |
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Publishing Year |
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1432 AH
2011 AD |
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Article Type |
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Article |
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Added Date |
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Monday, February 20, 2012 |
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Researchers
| S Sadiq Basha | Basha, S Sadiq | Researcher | Doctorate | drssb@yahoo.com |
| نصير شهزاد | Shahzad, Naseer | Researcher | Doctorate | nshahzad@kau.edu.sa |
| R Jeyaraj | Jeyaraj, R | Researcher | Doctorate | royerjeyaraj@yahoo.com |
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