If X is a complete metric space, the collection of all non-empty compact subsets of X forms a complete metric space (H(X), h), where h is the Hausdorff metric. In this paper we explore some of the geometry of the space H(Rn). Specifically, we concentrate on understanding lines in H(R). In particular, we show that for any two points A, B ∈ H(Rn), there exist infinitely many points on the line jo...

‎in this paper we study the existence of fixed points for mappings defined on complete metric spaces‎, ‎satisfying a general contractive inequality depending on two additional mappings‎.

In this paper, by using C-class functions, we will present a coupled …xed problem in b-metric space for the single-valued operators satisfying a generalized contraction condition. First part of the paper is related to some …xed point theorems, the second part presents the uniqueness and existence for the solution of the coupled …xed point problem and in the third part we...

We unify the concepts of G-metric, metric-like, and b-metric to define new notion of generalized b-metric-like space and discuss its topological and structural properties. In addition, certain fixed point theorems for two classes of G-α -admissible contractive mappings in such spaces are obtained and some new fixed point results are derived in corresponding partially ordered space. Moreover, so...

a projective parameter of a geodesic as solution of certain ode is defined to be a parameter which is invariant under projective change of metric. using projective parameter and poincaré metric, an intrinsic projectively invariant pseudo-distance can be constructed. in the present work, solutions of the above ode are characterized with respect to the sign of parallel ricci tensor on a finsler s...

in this paper, tripled coincidence points of mappings satisfying  -contractive conditions in the framework of partially ordered gb-metric spaces are obtained. our results extend the results of aydi et al. [h. aydi, e. karapnar and w. shatanawi, tripled xed point results in generalized metric space, j. applied math., volume 2012, article id 314279, 10 pages]. moreover, some examples of the mai...

In this paper, we give the idea of a generalized c-distance in a cone b-metric space. Then, we prove some common fixed point and fixed point theorems in cone b-metric spaces by using the distance.

Let (X,d,K) be a cone b-metric space over a ordered Banach space (E, ) with respect to cone P. In this paper, we study two problems: (1) We introduce a b-metric ρc and we prove that the b-metric space induced by b-metric ρc has the same topological structures with the cone b-metric space. (2) We prove the existence of the coincidence point of two mappings T , f : X → X satisfying a new quasi-co...

The time-optimal trajectory for an airplane from some starting point to some final point is studied by many authors. Here, we consider the extension of robot planer motion of Dubins model in three dimensional spaces. In this model, the system has independent bounded control over both the altitude velocity and the turning rate of airplane movement in a non-obstacle space. Here, in this paper a g...

In [Fuzzy Sets and Systems 27 (1988) 385-389], M. Grabiec in- troduced a notion of completeness for fuzzy metric spaces (in the sense of Kramosil and Michalek) that successfully used to obtain a fuzzy version of Ba- nachs contraction principle. According to the classical case, one can expect that a compact fuzzy metric space be complete in Grabiecs sense. We show here that this is not the case,...