We prove that the Hodge metric completion of the Teichmüller space of polarized and marked Calabi–Yau manifolds is a complex affine manifold. We also show that the extended period map from the completion space is injective into the period domain, and that the completion space is a domain of holomorphy and admits a complete Kähler-Einstein metric.

In this paper, we propose a new definition of intuitionistic fuzzyquasi-metric and pseudo-metric spaces based on intuitionistic fuzzy points. Weprove some properties of intuitionistic fuzzy quasi- metric and pseudo-metricspaces, and show that every intuitionistic fuzzy pseudo-metric space is intuitionisticfuzzy regular and intuitionistic fuzzy completely normal and henceintuitionistic fuzzy nor...

The Sylvester-Gallai theorem asserts that every finite set S of points in two-dimensional Euclidean space includes two points, a and b, such that either there is no other point in S is on the line ab, or the line ab contains all the points in S. V. Chvátal extended the notion of lines to arbitrary metric spaces and made a conjecture that generalizes the Sylvester-Gallai theorem. In the present ...

We establish some common fixed point results for multivalued mappings satisfying generalized contractive conditions on a complete partial metric space. The presented theorems extend some known results to partial metric spaces. We motivate our results by some given examples and an application for finding the solution of a functional equation arising in dynamic programming. 2000 Mathematics Subje...

This paper involves extended b ? metric versions of a fractional differential equation, system equations and two-dimensional (2D) linear Fredholm integral equations. By various given hypotheses, exciting results are established in the setting an id="M2"> space. Thereafter, by making consequent use fixed point te...

In this paper, we provide a generalization of rectangular b-metric space by relaxing the inequality to include unequal weights. We examples and restrictions for Lipschitz constant enabling convergence some sequences in proof fixed point theorems.

This paper is an attempt to introduce mathematical structures for classical planning. It is rst shown that the set-based structures underlying classical planning are unable to build more than a monoid. Consequently, an appropriate structure is presented (that of the incidence algebra of a partial plan) and used to build the partial plan space as an algebraic eld. A vector space, an aane space a...