In this paper, by using the following implicit relation, we examine the existence of a coupled coincidence point theorem for mappings F : X × X → X and g : X → X in the context of a partial metric space, where F has the mixed g-monotone property and F, g are O-compatible.
Very recently, Bhayo and Sándor [11], Corollary 3, again proved the Becker-Stark inequalities (1.4) by using Redheffer inequality (1.1), which reveals the implicit relation between Redheffer's and Becker-Stark's inequalities.
Then it is easy to see that F ⊂ A φ, which implies that the implicit relation of Definition 2.5 is a generalization of Aliouche and Fisher [[13], implicit relation].
First, we give a slight generalization of some of the results of the above papers using an implicit relation in the following way.
Now we give a fixed point theorem for two weakly increasing mappings in ordered metric spaces using an implicit relation.
In this paper, by using an implicit relation due to Rao et al. [12], we prove some common fixed point theorems for weakly compatible mappings with common limit range property.
Swanson's Undiscovered Public Knowledge (UPK) model (a.k.a. ABC model) was to discover the implicit relations among biological entities such as magnesium, epilepsy, and migraine.
Therefore, we give a common fixed point theorem for two weakly increasing operators in partially ordered metric spaces using implicit relation technique.
In Section 2, we prove a coincidence point theorem where we use an implicit relation only for comparable elements of a partially ordered set X. Our result generalizes/extends [1 3, 23, 24] work to partial ordered sets.
Recently, Altun and Simsek [4] proved the fixed point results using implicit relations for one map and two maps and generalized the results given in [3, 25, 27, 28].
