This paper deals with some issues of fixed point concerning Caristi type mappings introduced by Abbasi and Golshan (Kybernetika 52:929–942, 2016) in fuzzy metric spaces. We enlarge this class prove completeness characterization corresponding space. The includes a comprehensive set examples showing the generality our results an open question.

This is a partial account of the fascinating history of Distance Geometry. We make no claim to completeness, but we do promise a dazzling display of beautiful, elementary mathematics. We prove Heron’s formula, Cauchy’s theorem on the rigidity of polyhedra, Cayley’s generalization of Heron’s formula to higher dimensions, Menger’s characterization of abstract semi-metric spaces, a result of Gödel...

Noether symmetries provide conservation laws that are admitted by Lagrangians representing physical systems. For partial differential equation possessing Lagrangians these symmetries are obtained by the invariance of the corresponding action integral. In this paper we provide a systematic procedure for determiningNoether symmetries and conserved vectors for a Lagrangian constructed from a Loren...

We construct a distance on the moduli space of symplectic toric manifolds of dimension four. Then we study some basic topological properties of this space, in particular, connectedness, compactness and completeness. The construction of the distance is related to the DuistermaatHeckman measure and the Hausdorff metric. While the moduli space, its topology and metric, may be constructed in any di...

The IFS is a scheme for describing and manipulating complex fractal attractors using simple mathematical models. More precisely, the most popular “fractal –based” algorithms for both representation and compression of computer images have involved some implementation of the method of Iterated Function Systems (IFS) on complete metric spaces. In this paper a new generalized space called Multi-Fuz...

It is known since 1973 that Lawvere’s notion of (Cauchy-)complete enriched category is meaningful for metric spaces: it captures exactly Cauchy-complete metric spaces. In this paper we introduce the corresponding notion of Lawvere completeness for (T,V)-categories and show that it has an interesting meaning for topological spaces and quasi-uniform spaces: for the former ones means weak sobriety...

The purpose of this paper is to study common fixed point theorems for six (four single-valued and two set-valued) mappings in fuzzy metric space using general contractive condition of integral type, without assuming compatibility and continuity of any mapping on non complete metric spaces. To prove the theorems, we use a non compatible condition, that is, weak commutativity of type (Kh)in fuzzy...

According to Schoen and Yau (1988), an extensive class of conformally flat manifolds is realized as Kleinian manifolds. Nayatani (1997) constructed a metric on a Kleinian manifold M which is compatible with the canonical flat conformal structure. He showed that this metric gN has a large symmetry if gN is a complete metric. Under certain assumptions including the completeness of gN , the isomet...

After the definition of the concept of fuzzy metric space by some authors 1–3 , the fixed point theory on these spaces has been developing see, e.g., 4–9 . Generally, this theory on fuzzy metric space is done for contractive or contractive-type mappings see 2, 10–13 and references therein . In this paper we introduce the concept of fuzzy order ψ-contractive mappings and give two fixed point the...