Search

Fixed-point theory, which has been developing since 1922, is widely used. Various contraction principles have been defined in the literature. In this work, we define rational-type contraction and weak Choudhury type contraction using α -series in F-metric spaces and prove common fixed-point theorems for sequences of self-mappings. This method is based on the convergence series of coefficients. Our results are the generalized version of the results in the literature. Finally, we apply our main results to solve an integral equation and a differential equation. [ABSTRACT FROM AUTHOR]

Isik and Turkoglu [Some Fixed Point Theorems in Ordered Partial Metric Spaces, Journal of Inequalities and Special Functions, Volume 4 Issue 2(2013), Pages 13-18] established new fixed point results in complete partial metric spaces. The purpose of this paper is to introduce a dual contraction of rational type and to obtain some new fixed point results in dual partial metric spaces for dominating and dominated mappings. These results extend various comparable results existing in literature. Moreover, we give an example that shows the usefulness and effectiveness of these results among corresponding fixed point theorems established in partial metric spaces.

In this paper, we introduce the notion of generalized weakly α-contractive mappings and give some common fixed point results for this type of contraction. The presented theorems extend, generalize and improve many existing results in the literature. Two examples as well as an application to ordinary differential equations are also given in order to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we use the order relation on uniform spaces defined by [5] to introduce the notion of compatibility of mappings in an ordered uniform space and use this notion to establish coupled coincidence point theorems to ordered uniform space. An example is also given. [ABSTRACT FROM AUTHOR]

In this paper, we proved a fixed point theorem and a common fixed point theorem in cone metric spaces for generalized contraction mappings where some of the main results of Ćirić in [8, 27] are recovered. [ABSTRACT FROM AUTHOR]

In recent years several fixed point results have been obtained on metrically convex spaces. Assad and Kirk [6] gave a sufficient condition enunciating fixed point of set-valued mappings enjoying specific boundary condition in metrically convex metric spaces. A significant generalization of the fixed point theorem of Assad [5] and the theorem of Assad and Kirk [6] for multivalued contraction non-self mappings is obtained by Itoh [17] in 1977. In the current years the work due to Assad and Kirk [6] has inspired extensive activities which includes Ahmad and Imdad [1], [2], Imdad et al. [13], Imdad and Ali [14], Itoh [17], Khan [19] and some others. Most recently, Dhage et al. [9] and Huang and Cho [12] proved some fixed point theorems for a sequence of set-valued mappings which generalize several results due to Ahmad and Khan [3], Itoh [17], Khan [19] and others. The purpose of this paper is to prove some coincidence and common fixed point theorems for multivalued mappings satisfying an implicit relation on metrically convex spaces. Our results either partially or completely generalize earlier results due to Ahmad and Imdad [1], [2], Ahmad and Khan [3], Ćirić [7], Imdad and Khan [15], Itoh [17], Khan [19], Khan et al. [20], Rhoades [26] and several others. See also the related Theorem 3.1 of [14]. [ABSTRACT FROM AUTHOR]

In this paper, we use the order relation on partial metric spaces defined by [1] to prove some new fixed point theorems for multivalued monotone mappings in ordered partial metric spaces. [ABSTRACT FROM AUTHOR]