Some Results on Fixed Points

On the method of successive approximations <o metode posledovatel'nykh priblizheniy<

We study some minimization problems for noncyclic mappings in metric spaces. We then apply the solution to obtain some results in the theory of analytic functions.

Global Optimal Solutions of Noncyclic Mappings in Metric Spaces

Let A and B be two nonempty subsets of a metric space (X,d). A best proximity point of a non-self-mapping T:A→B is a point x⁎∈A satisfying the equality d(x⁎,Tx⁎)=d(A,B), where d(A,B)=inf{d(a,b):a∈A,b∈B}. In this paper, we introduce a new concept of α–ψ-proximal contractive type mappings and establish best proximity point theorems for such mappings in complete metric spaces. Several applications and interesting consequences of our obtained results are presented.

Best proximity points for α–ψ-proximal contractive type mappings and applications

Best proximity points of cyclic mappings

In this paper we consider a cyclic mapping on a partially ordered complete metric space. We prove some fixed point theorems, as well as some theorems on the existence and convergence of best proximity points.

Best Proximity Points for Cyclic Mappings in Ordered Metric Spaces

Let A, B be nonempty subsets of a metric space (X, d) and T : A → 2B be a multivalued non-self-mapping The purpose of this paper is to establish some theorems on the existence of a point \({x^*\in A}\) , called best proximity point, which satisfies \({{\rm inf}\{d(x^*,y):y\in Tx^*\}=dist(A,B)}\) This will be done for contraction multivalued non-self-mappings in metric spaces, as well as for nonexpansive multivalued non-self-mappings in Banach spaces having appropriate geometric property

The existence of best proximity points for multivalued non-self-mappings

In this paper, we prove the existence and convergence of best proximity points for asymptotic cyclic contractions in metric spaces with the property UC, as well as for asymptotic proximal pointwise contractions in uniformly convex Banach spaces. Moreover, we consider a generalized cyclic contraction mapping and prove the existence of best proximity points for such a mapping in Banach spaces which do not necessarily satisfy the geometric property UC.

Best proximity points for asymptotic cyclic contraction mappings

We prove a best proximity point theorem for proximal generalized contractive type mappings in metric spaces, which is a generalization of recent best proximity point theorems and some famous fixed point theorems due to Berinde and Suzuki. We also introduce a new class of proximal non-self mappings and obtain sufficient conditions, which ensure the existence of a best proximity point. Moreover, we define algorithms and prove that they find a best proximity point for these classes of non-self mappings in the setting of metric and Banach spaces.

Moosa Gabeleh

Papers

Global Optimal Solutions of Noncyclic Mappings in Metric Spaces

Best Proximity Points for Cyclic Mappings in Ordered Metric Spaces

The existence of best proximity points for multivalued non-self-mappings

Best proximity points for asymptotic cyclic contraction mappings

Best Proximity Point Theorems via Proximal Non-self Mappings