Best Proximity Results on Dualistic Partial Metric Spaces

Abstract

We introduce the generalized almost ( φ , θ ) -contractions by means of comparison type functions and another kind of mappings endowed with specific properties in the setting of dualistic partial metric spaces. Also, generalized almost θ -Geraghty contractions in the setting of dualistic partial metric spaces are defined by the use of a function of Geraghty type and another adequate auxiliary function. For these classes of generalized contractions, we have stated and proved the existence and uniqueness of a best proximity point.

On Coupled Best Proximity Points in Reflexive Banach Spaces

“…In this context, the notions of coupled fixed points [5] and coupled best proximity points for an ordered pair (F, G), F : A × A → B, G : B × B → A, where A, B ⊂ X [6,7] are relevant. Deep results in the theory of coupled fixed points, for example, can be found in [2,[8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23].…”

Interpolative Prešić Type Contractions and Related Results

“…). e existence of such points of nonself maps has been discussed by several researchers in different ways, for example, Caballero et al [22] studied the existence of best proximity points for nonself maps satisfying Geraghty contraction and P-property in metric spaces, Bilgili et al [23], Aydi et al [24], and Pitea [25] extended the work of Caballero et al [22] by introducing generalized Geraghty contraction, ψ-Geraghty contraction and generalized almost θ-Geraghty contraction for nonself maps, Basha and Shahzad [26] and Basha [27] defined proximal-type contractions to study the existence of best proximity points, Jleli and Samet [28] defined α-ψ-proximal contraction to ensure the existence of best proximity points, Jleli et al [29] and Aydi et al [30] defined generalized α-ψ-proximal contractions to extend the work of Jleli and Samet [28], Abkar and Gabeleh [31] and Kumam et al [32] studied the existence of best proximity points for multivalued nonself maps in metric spaces, Ali et al [33] defined implicit proximal contractions, Sahin et al [34] defined proximal nonunique contraction, and Ali et al [35] studied the existence of best proximity points for Prešić type nonself operators satisfying proximal type contractions.…”

Quadruple g-best Proximity Point for New Contraction in Complete Metric Space

“…Motivated from [18], Rohen and Maliki [17] gave the notion of tripled best proximity points theorem graced with P-property and the developed contraction. See references [15], [2], [9], [14] for further research in coupled best proximity point results.…”