Abstract
In this paper, we define the weak P-property and the α-ψ-proximal contraction by p in which p is a τ-distance on a metric space. Then, we prove some best proximity point theorems in a complete metric space X with generalized distance. Also we define two kinds of α-p-proximal contractions and prove some best proximity point theorems.
Highlights
Let us assume that A and B are two nonempty subsets of a metric space (X, d) and T : A −→ B
Suzuki [ ] introduced the concept of τ -distance on a metric space and proved some fixed point theorems for various contractive mappings by τ -distance
By using the concept of τ -distance, we prove some best proximity point theorems
Summary
Let us assume that A and B are two nonempty subsets of a metric space (X, d) and T : A −→ B. 3 Some best proximity point theorems we define the weak P-property with respect to a τ -distance as follows. Suppose that p is a τ -distance on X and T : A −→ B satisfies the following conditions: (a) T(A ) ⊆ B and (A, B) has the weak P-property with respect to p.
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