let $p$ be an analytic function defined on the open unit disc $mathbb{d}$ with $p(0)=1.$ the conditions on $alpha$ and $beta$ are derived for $p(z)$ to be subordinate to $1+4z/3+2z^{2}/3=:varphi_{c}(z)$ when $(1-alpha)p(z)+alpha p^{2}(z)+beta zp'(z)/p(z)$ is subordinate to $e^{z}$. similar problems were investigated for $p(z)$ to lie in a region bounded by lemniscate of bernoulli $|w^{2}-1...

In this paper, a new weighted identity for differentiable functions of two variables defined on a rectangle from the plane is established. By using the obtained identity and analysis, some new weighted integral inequalities for the classes of co-ordinated convex, co-ordinated wright-convex and co-ordinated quasi-convex functions on the rectangle from the plane are established which provide weig...

OBJECTIVE The aim of this study was to assess the accuracy of a newly developed three-dimensional (3D) imaging system in recording facial morphology. METHODS Twenty-one infants with cleft lip each had a full-face alginate impression taken at the time of primary lip repair, and a stone cast was constructed from each impression. Five anthropometric points were marked on each cast. Each cast was...

A (t, s, v)-all-or-nothing transform is a bijective mapping defined on s-tuples over an alphabet of size v, which satisfies the condition that the values of any t input co-ordinates are completely undetermined, given only the values of any s− t output co-ordinates. The main question we address in this paper is: for which choices of parameters does a (t, s, v)-all-or-nothing transform (AONT) exi...

Let % be a preference relation on a convex set F . Necessary and sufficient conditions are given that guarantee the existence of a set {ul} of affine utility functions on F such that % is represented by U ( f ) = ul ( f ) if f ∈ Fl; where each Fl is a convex subset of F . The interpretation is simple: facing a “non-homogeneous” set F of alternatives, a decision maker splits it into “homogeneous...

Although prox-regular functions in general are nonconvex, they possess properties that one would expect to find in convex or lowerC2  functions. The class of prox-regular functions covers all convex functions, lower C2  functions and strongly amenable functions. At first, these functions have been identified in finite dimension using proximal subdifferential. Then, the definition of prox-regula...