Recently, Phiangsungnoen et al. [J. Inequal. Appl.2014: 201 (2014)] studied fuzzy mappings in the framework of Hausdor fuzzy metric spaces. Following this direction of research, we establish the existence of fixed fuzzy points of fuzzy mappings. An example is given to support the result proved herein; we also present a coincidence and common fuzzy point result.Finally, as an application of our results, we investigate the existence of solution for some recurrence relations associated to the analysis of quicksort algorithms.

In the study of fixed points of an operator it is useful to consider a more general concept, namely coupled fixed point. Edit In this paper, by using notion partial metric, we introduce a metric space $S$-Hausdorff on the set of all close and bounded subset of $X$. Then the fixed point results of multivalued continuous and surjective mappings are presented. Furthermore, we give a positive result on the Nadler contraction theorem for multivalued mappings in this space. In the following, by expressing pseudo-Banach-type pairs of mappings, we study the conditions for the existence of a unique coupled strong fixed point in these mappings. Pseudo-Chatterjae mapping $F: X \times X\to X$ satisfies in \[d\left( F(x, y), F(u, v) \right) \leq k \max \left\{ d\left( x, F(u, v)\right), d\left( F(x, y), u\right) \right\}, \] where $x, v \in A$, $y, u \in B$ and $0 < k < \frac{1}{2}$. Also, We define some quasi-Banach and Pseudo-Chatterjae contraction inequalities. In addition, we will prove theorems about coupled fixed points. Finally, several examples are presented to understand the our results.

We define and study a quantale-valued Wijsman structure on the hyperspace of all non-empty closed sets of a quantalevalued metric space. We show its admissibility and that the metrical coreflection coincides with the quantale-valued Hausdorff metric and that, for a metric space, the topological coreflection coincides with the classical Wijsman topology. We further define an index of compactness and show that the indices of compactness of the quantale-valued metric space and of the hyperspaces equipped with the quantale-valued Hausdorff metric and with the quantale-valued Wijsman structure coincide.

In this paper, we introduce a new condition namely, the (W.C.C) condition and give some Suzuki-type, unique, common fixed-point theorems for pairs of hybrid mappings in partial metric spaces using a partial Hausdorff metric. These results generalize and extend the several comparable results in this literature in metric and partial metric spaces.

This paper introduces a novel concept of KM-single valued neutrosophic Hausdorff space and KM-single valued neutrosophic manifold space. This study generalizes the concept of KM-single valued neu-trosophic manifold space to union and product of KM-single valued neu-trosophic manifold space and in this regard investigates some product of KM-single valued neutrosophic manifold spaces. Indeed, this study analyses the notation of KM-single valued neutrosophic manifold based on a valued-level subset.

Endpoint results are presented for multi{valued cyclic contraction mappings on complete metric spaces (X; d). Our results extend previous results given by Nadler (1969), Da er{Kaneko (1995), Harandi (2010), Moradi and Kojasteh (2012) and Karapinar (2011).

In this paper we introduce entire sequence spaces defined by a sequence of modulus functions F=(¦k) We study some topological properties of these spaces and prove some inclusion relations.