We first establish some new critical point theorems for nonlinear dynamical systems in cone metric spaces or usual metric spaces, and then we present some applications to generalizations of DancšHegedüs-Medvegyev’s principle and the existence theorem related with Ekeland’s variational principle, Caristi’s common fixed point theorem for multivalued maps, Takahashi’s nonconvex minimization theore...

Probabilistic metric space was first introduced by Menger [6]. Later, there are many authors who have some detailed discussions and applications of a probabilistic metric space, for example, we may see Schweizer and Sklar [8]. Besides, there are many results about fixed point theorems in a probabilistic metric space with contractive types having appeared; we may see the papers [1–3, 9–12]. In t...

Abstract_ _ We prove a common coincidence point theorem for a non-fuzzy mapping and a pair of fuzzy mappings under a ' contraction condition on a metric space in the context of Hausdor¤ metric on the family of fuzzy sets. Further, we establish a common coincidence point theorem on a metric space with the d1 metric on fuzzy sets, which extends a number of recent results. As applications, we obta...

In this paper, following a new interpolation approach in fixed point theory, we introduce the concepts of interpolative Hardy-Rogers-type fuzzy contraction and Reich-Rus-Ciric type framework metric spaces, analyze existence points for such contractions equipped with some suitable hypotheses. A few consequences single-valued mappings which include conclusion main result Karapinar et al. [On Hard...

The fixed point theorems in metric spaces are playing a major role to construct methods in mathematics to solve problems in applied mathematics and sciences. So the attraction of metric spaces to a large numbers of mathematicians is understandable. Some generalizations of the notion of a metric space have been proposed by some authors. In 2006, Mustafa in collaboration with Sims introduced a ne...

Let A and B be two nonempty subsets of a metric space X. A mapping T : A∪B → A∪B is said to be noncyclic if T (A) ⊆ A and T (B) ⊆ B. For such a mapping, a pair (x, y) ∈ A×B such that Tx = x, Ty = y and d(x, y) = dist(A,B) is called a best proximity pair. In this paper we give some best proximity pair results for noncyclic mappings under certain contractive conditions.

Using the concept of a mixed g-monotone mapping, we prove some coupled coincidence and coupled common fixed point theorems for nonlinear contractive mappings in partially ordered complete quasi-metric spaces with a Q-function q. The presented theorems are generalizations of the recent coupled fixed point theorems due to Bhaskar and Lakshmikantham 2006 , Lakshmikantham and Ćirić 2009 and many ot...