Abstract
In this paper, we prove some quadrupled best proximity point theorems in partially ordered metric space by using (𝜓,𝜙) contraction. Our results generalise the results of Kumam et.al. (Coupled best proximity points in ordered metric spaces, Fixed point Theory and Application 2014, 2014:107). An example is also given to verify the results obtained.
Highlights
In this paper, we prove some quadrupled best proximity point theorems in partially ordered metric space by using (ψ, φ) contraction
Our results generalise the results of Kumam et al (Coupled best proximity points in ordered metric spaces, Fixed Point Theory and Application 2014, 2014:107)
In a metric space (X, d) a self mapping T on X is said to posses fixed point if the equation Tx = x has at least one solution
Summary
Abstract: In this paper, we prove some quadrupled best proximity point theorems in partially ordered metric space by using (ψ, φ) contraction. If (X, ⪯ ) is a partially ordered set, the mapping F is said to have the mixed monotone property, if x1,x2 ∈ X, x1 ⪯ x2 ⟹ F(x1, y, z, w) ⪯ F(x2, y, z, w), y, z, w ∈ X, y1, y2 ∈ X, y1 ⪯ y2 ⟹ F(x, y1, z, w) ⪰ F(x, y2, z, w), x, z, w ∈ X, z1, z2 ∈ X, z1 ⪯ z2 ⟹ F(x, y, z1, w) ⪯ F(x, y, z2, w), x, y, w ∈ X, w1,w2 ∈ X, w1 ⪯ w2 ⟹ F(w, y, z, w1) ⪰ F(x, y, z, w2), x, y, z, ∈ X, Let A and B be non empty subsets of a metric space(X, d).
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