A Note on Existence and Convergence of Best Proximity Points for Pointwise Cyclic Contractions |
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| Authors: | G. Sankara Raju Kosuru P. Veeramani |
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| Affiliation: | 1. Department of Mathematics , Indian Institute of Technology Madras , Chennai , India rajuiitmadras@gmail.com;3. Department of Mathematics , Indian Institute of Technology Madras , Chennai , India |
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| Abstract: | We introduce a notion of pointwise cyclic contraction T satisfying TA ? B and TB ? A to obtain the existence of a point x ∈ A, such that d(x, Tx) = dist(A, B), known as a best proximity point for such a map. We also prove that for any x ∈ A, the Picard iteration {T2nx} converges to a best proximity point. |
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| Keywords: | Best proximity points Pointwise cyclic contraction Projectional property Semi sharp proximinal pair |
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