In this study, we aim to introduce the notion of fuzzy partial metric spaces which is a generalization crisp in fuzzifying view with distance between ordinary points. For aim, first present concept by considering as non-negative, upper semi-continuous, normal and convex numbers giving examples. We obtain some useful inequalities under restrictions spaces. Then discuss relationships other struct...

This article presents some new inequalities of Simpson’s type for differentiable functions by using (α,m)-convexity. Some results concavity are also obtained. These estimates improve on the previously known ones. applications special means real numbers provided.

We compute the hessian iddW of the natural metric form W on the twistor space T(M, g) of a 4-dimensional Riemannian manifold (M, g). We then adapt the computations to the case of the twistor space T(M, g,D) of a hyperkähler manifold (M, g,D = (I, J,K)). We show a strong positivity property of the hessian iddW on the twistor space T(M, g,D) and prove, as an application, a convexity property of t...

An M-space is a metric space (X, d) having the property that for each pair of points p, q ∈ X with d(p, q) = λ and for each real number α ∈ [0, λ], there is a unique rα ∈ X such that d(p, rα) = α and d(rα, q) = λ − α. In an M-space (X, d), we say that metric segments have unique prolongations if points p, q, r, s satisfy d(p, q) + d(q, r) = d(p, r), d(p, q) + d(q, s) = d(p, s) and d(q, r) = d(q...

Having a prior assumption about where light originates can disambiguate perceptual scenarios. Previous studies have reported that adult observers use a "light-from-above" prior as well as a convexity prior to constrain perception of shape from shading. Such priors may reflect information acquired about the visual world, where objects tend to be convex and light tends to come from above. In the ...

On arbitrary spacetimes, we study the characteristic Cauchy problem for Dirac fields on a light-cone. We prove the existence and uniqueness of solutions in the future of the light-cone inside a geodesically convex neighbourhood of the vertex. This is done for data in L 2 and we give an explicit definition of the space of data on the light-cone producing a solution in H 1. The method is based on...

The present experiment was designed to examine the roles of painted linear perspective cues, and the convexity bias that are known to influence human observers' perception of three-dimensional (3D) objects and scenes. Reverse-perspective stimuli were used to elicit a depth-inversion illusion, in which far points on the stimulus appear to be closer than near points and vice versa, with a 2 (Type...

Our visual system faces the challenging task to construct integrated visual representations from the visual input projected on our retinae. Previous research has provided mixed evidence as to whether visual awareness of the stimulus parts is required for such integration to occur. Here, we address this issue by taking a novel approach in which we combine a monocular rivalry stimulus (i.e., a bi...

A law invariant risk measure ρ has the Convex Levels Sets property (CxLS) if ρ(F ) = ρ(G) = γ ⇒ ρ(λF + (1− λ)G) = γ, for each γ ∈ (0, 1). The level sets of ρ are convex with respect to mixtures of distributions; such a convexity has not to be confused with convexity or quasi-convexity with respect to sums of random variables. In the axiomatic theory of risk measures, the CxLS property arises na...