A new class of \(\mathcal{S}\)-contractions in complete metric spaces and \(\mathcal{G_{P}}\)-contractions in ordered metric spaces
The authors introduce the notions of \(S\)-contractions and \({\mathcal G}_P\)-contractions and prove the following results. Let \(A\), \(B\) be nonempty closed subsets of \(X\). If \(S,T: A\to B\) are \(S\)-contractions satisfying some conditions in a complete metric space \((X,d)\), then there exists a unique common best proximity point \(x\in A\) such that \(d(x, Tx)= d(A, B)= d(x, Sx)\). If \(f: A\to B\) is a \({\mathcal G}_P\)-contraction satisfying some conditions in a complete partially ordered metric space \((X,\preccurlyeq, d)\), then there exists a unique point \(x\in A\) such that \(d(x,fx)= d(A,B)\).
scientific article; zbMATH DE number 6610397
scientific article