and Applied Analysis 3 Definition 1.11 see 4 . Let f and g be two self-mappings from a G-metric space X,G into itself. Then the mappings f and g are said to be weakly compatible if G fgx, gfx, gfx 0 whenever G fx, gx, gx 0. Proposition 1.12 see 1 . Let X,G be a G-metric space. Then, for all x, y, z, a in X, it follows that i if G x, x, y 0, then x y z; ii G x, y, z ≤ G x, x, y G x, x, z ; iii G...

Let (M, g) be an (n+1)-dimensional space time, with bounded curvature, with respect to a bounded framing. If (M, g) is vacuum, or satisfies a mild condition on the stress-energy tensor, then we show that (M, g) locally admits coordinate systems in which the Lorentz metric g is wellcontrolled in the (space-time) Sobolev space L, for any p <∞.

QQ(R) (abbreviated as Q) is the space of unordered Q points in R introduced by Almgren [AF]. In this paper, we first show that the space Q with metric G is non-negatively curved in the sense of Alexandrov. We also discuss some issues like metric tangent cone and exponential map. In the second part, we define the signature of points in Q, give a decomposition of this metric space according to th...

We investigate the existence of well-ordered sequences of Baire 1 functions on separable metric spaces. Any set F of real valued functions defined on an arbitrary set X is partially ordered by the pointwise order, that is f ≤ g iff f(x) ≤ g(x) for all x ∈ X. In other words put f < g iff f(x) ≤ g(x) for all x ∈ X and f(x) 6= g(x) for at least one x ∈ X. Our aim will be to investigate the possibl...

Let M be an n-dimensional projective algebraic manifold in certain projective space CP . The hyperplane line bundle of CP restricts to an ample line bundle L on M , which is called a polarization of M . A Kähler metric g is called a polarized metric, if the corresponding Kähler form represents the first Chern class c1(L) of L in H (M,Z). Given any polarized Kähler metric g, there is a Hermitian...

recently, cho et al. [y. j. cho, r. saadati, s. h. wang, common xed point theorems on generalized distance in ordered cone metric spaces, comput. math. appl. 61 (2011) 1254-1260] dened the concept of the c-distance in a cone metric space and proved some xed point theorems on c-distance. in this paper, we prove some new xed point and common xed point theorems by using the distance in ordere...

In this paper, we find the best proximity point in G-metric spaces for G-generalized ζ-β-T contraction mappings and verify existence uniqueness of complete G metric space using idea an approximatively compact set. addition, example is provided to illustrate outcome.

In this paper we define weak $F$-contractions on a‎ ‎metric space into itself by extending $F$-contractions‎ ‎introduced by D‎. ‎Wardowski (2012) and provide some fixed point‎ ‎results in complete metric spaces and in partially ordered complete ‎generalized metric spaces‎. ‎Some relationships between weak‎ ‎$F$-contractions and $Fi$-contractions are highlighted‎. ‎We also ‎give some application...

Recently, Cho et al. [Y. J. Cho, R. Saadati, S. H. Wang, Common xed point theorems on generalized distance in ordered cone metric spaces, Comput. Math. Appl. 61 (2011) 1254-1260] dened the concept of the c-distance in a cone metric space and proved some xed point theorems on c-distance. In this paper, we prove some new xed point and common xed point theorems by using the distance in ordered con...

a cartan manifold is a smooth manifold m whose slit cotangent bundle 0t *m is endowed with a regularhamiltonian k which is positively homogeneous of degree 2 in momenta. the hamiltonian k defines a (pseudo)-riemannian metric ij g in the vertical bundle over 0 t *m and using it, a sasaki type metric on 0 t *m is constructed. a natural almost complex structure is also defined by k on 0 t *m in su...