Best proximity points for Geraghty’s proximal contraction mappings

Abstract

In this paper, we generalized the notion of proximal contractions of the first and second kinds by using Geraghty's theorem and establish best proximity point theorems for proximal contractions. Our results improve and extend the recent results of Sadiq Basha and some others. MSC: 47H09; 47H10

Coincidence best proximity points for geraghty type proximal cyclic contractions

“…If we take α(x 0 , x 1 ) = 1 in Theorem 3.5, we obtain the following main result of [18]. Then there exists point x ∈ A and there exists point y ∈ B such that…”

“…In this section we generalized the notions of Mongkolkeha et al [18] and obtain coincidence best proximity point results. …”

“…Motivated by Basha [21], Mongkolkeha et al [18] introduced the new classes of proximal contractions, which are more general than the class of proximal contractions of the first and second kinds. In this section we generalized the notions of Mongkolkeha et al [18] and obtain coincidence best proximity point results.…”

Fixed point theorems for generalized α−η−ψ− Geraghty contraction type mappings in α−η− complete metric spaces

“…There were many authors have studied and proved the results for fixed point theory by generalizing the Banach contraction principle in several directions (see [2,3,4,5,6,7,8,9,10,11,12] and references contained therein). One of the remarkable result is Geraghty's theorem given by Geraghty [4].…”

Fixed points for φE-Geraghty contractions

“…It is know that BCP has been extended in many various directions by several authors, see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and the references therein. The following generalization is due to Geraghty [7].…”