Common fixed points for generalized contractive mappings in cone metric spaces

The purpose of this paper is to establish coincidence point and common fixed point results for four maps satisfying generalized weak contractions in cone metric spaces. Also, an example is given to illustrate our results

Nonlinear generalized cyclic contractions in complete G-metric spaces and applications to integral equations

In this paper we introduce generalized cyclic contractions in G-metric spaces and establish some fixed point theorems. The presented theorems extend and unify various known fixed point results. Examples are given in the support of these results. Finally, an application to the study of existence and uniqueness of solutions for a class of nonlinear integral equations is given

Extension of Darbo’s fixed point theorem via shifting distance functions and its application

In this paper, we discuss solvability of infinite system of fractional integral equations (FIE) of mixed type. To achieve this goal, we first use shifting distance function to establish a new generalization of Darbo’s fixed point theorem, and then apply it to the FIEs to establish the existence of solution on tempered sequence space. Finally, we verify our results by considering a suitable example

Common fixed point theorems via common limit range property in symmetric spaces under generalized Phi-contractions

The aim of this paper is to use common limit range property for a quadruple of non-self mappings for deriving common fixed point results under a generalized Φ-contraction condition in symmetric spaces. Some examples are given to exhibit different types of situations where these conditions can be used and to distinguish our results from the known ones. As an application, an existence result for certain systems of integral equations is presented

Common fixed points versus invariant approximation for noncommutative mappings

The aim of this paper is to obtain common fixed points as invariant approximation for noncommuting two pairs of mappings. As consequences, our works generalize the recent works of Nashine [9] by weakening commutativity hypothesis and by increasing the number of mappings involved

Coupled common fixed point theorems for a pair of commuting mappings in partially ordered complete metric spaces

AbstractThe purpose of this paper is to establish a coupled coincidence point for a pair of commuting mappings in partially ordered complete metric spaces. We also present a result on the existence and uniqueness of coupled common fixed points. An example is given to support the usability of our results

Cyclic-Prešić–Ćirić operators in metric-like spaces and fixed point theorems

In this paper, we define the cyclic-Prešić–Ćirić operators in metric-like spaces and prove some fixed point results for such operators. Our results generalize that of S.B. Prešić [Sur une classe d'inéquations aux différences finite et sur la convergence de certaines suites, Publications de l'Institut Mathématique (N.S.), 5(19):75–78, 1965] and several later results. An example is given which shows that the results proved herein are the proper generalizations of existing ones

Generalized Altering Distances and Common Fixed Points in Ordered Metric Spaces

Coincidence point and common fixed point results with the concept of generalized altering distance functions in complete ordered metric spaces are derived. These results generalize the existing fixed point results in the literature. To illustrate our results and to distinguish them from the existing ones, we equip the paper with examples. As an application, we study the existence of a common solution to a system of integral equations

EXISTENCE OF BEST PROXIMITY POINTS: GLOBAL OPTIMAL APPROXIMATE SOLUTION

Abstract. Given non-empty subsets A and B of a metric space, let S : A → B and T : A → B be non-self mappings. Taking into account the fact that, given any element x in A, the distance between x and Sx, and the distance between x and T x are at least d(A, B), a common best proximity point theorem affirms global minimum of both functions x → d(x, Sx) and x → d(x, T x) by imposing a common approximate solution of the equations Sx = x and T x = x to satisfy the constraint that d(x, Sx) = d(x, T x) = d(A, B). In this work we introduce a new notion of proximally dominating type mappings and derive a common best proximity point theorem for proximally commuting non-self mappings, thereby producing common optimal approximate solutions of certain simultaneous fixed point equations when there is no common solution. We furnish suitable examples to demonstrate the validity of the hypotheses of our results