Best proximity point theorems for non-self proximal Reich type contractions in complete metric spaces


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	Best proximity point theorems for non-self proximal Reich type contractions in complete metric spaces


	Fixed Point Theory, Volume 19, No. 2, 2018, 449-452, June 1st, 2018 DOI: 10.24193/fpt-ro.2018.2.35 Authors: Clement Boateng Ampadu Abstract: Recall from [2], that a mapping T:X ↦ X is called a Reich mapping if it satisfies for all x,y ∈ X, d(Tx,Ty) ≤ ad(x,Tx)+bd(y,Ty)+cd(x,y), where a,b,c are nonnegative and satisfy a+b+c<1. Alternatively, one could define a Reich mapping as follows: T:X ↦ X is called a Reich mapping if there exists a nonnegative constant k with k < ⅓ such that d(Tx,Ty) ≤ k[d(x,Tx)+d(y,Ty)+d(x,y)]. In the present paper, we address the following: How do we characterize Theorem 3 [2], when T is a non-self map? We show such a characterization is given by Theorem 3.1 or Corollary 3.2 in this paper. Key Words and Phrases: Fixed point, best proximity point, contraction, proximal contraction, proximal cyclic contraction, Reich contraction. 2010 Mathematics Subject Classification: 47H10. Published on-line: June 1st, 2018. Abstract pdf Fulltext pdf Back to volume's table of contents