Let Z and X be Banach spaces, U ⊂ Z an open convex set and f : U → X a mapping. We say that f is a delta-convex mapping (d. c. mapping) if there exists a continuous convex function h on U such that y ◦ f + h is a continuous convex function for each y ∈ Y , ‖y∗‖ = 1. We say that f : U → X is locally d. c. if for each x ∈ U there exists an open convex U ′ such that x ∈ U ′ ⊂ U and f |U ′ is d. c....

Column-convex polyominoes were introduced in 1950’s by Temperley, a mathematical physicist working on “lattice gases”. By now, column-convex polyominoes are a popular and well-understood model. There exist several generalizations of column-convex polyominoes. However, the enumeration by area has been done for only one of the said generalizations, namely for multi-directed animals. In this paper...

In this paper we analyze the local and global boundary rigidity problem for general Riemannian manifolds with $(M,g)$. We show that distance function, i.e., $d_g|_{\partial M \times \partial M}$, known near a point $p\in M$ at which $\partial is strictly convex, determines $g$ in suitable neighborhood of $p$ $M$, up to natural diffeomorphism invariance problem. also consider closely related len...

Let $Omega_X$ be a bounded, circular and strictly convex domain of a Banach space $X$ and $mathcal{H}(Omega_X)$ denote the space of all holomorphic functions defined on $Omega_X$. The growth space $mathcal{A}^omega(Omega_X)$ is the space of all $finmathcal{H}(Omega_X)$ for which $$|f(x)|leqslant C omega(r_{Omega_X}(x)),quad xin Omega_X,$$ for some constant $C>0$, whenever $r_{Omega_X}$ is the M...

We introduce the notion of $m$-polynomial harmonically convex interval-valued function. A relationship between a given function and its component real-valued functions is pointed out. Moreover, some new Hermite--Hadamard type results are established for this class functions. Our complement extend existing in literature. By taking $m\geq 2$, we derive loads interesting inclusions. anticipate tha...

We prove that the Robin ground state and torsion function are respectively log-concave $\frac{1}{2}$-concave on an uniformly convex domain $\Omega\subset \mathbb{R}^N$ of class $\mathcal{C}^m$, with $[m -\frac{ N}{2}]\geq 4$, provided parameter exceeds a critical threshold. Such threshold depends $N$, $m$, geometry $\Omega$, precisely diameter boundary curvatures up to order $m$.

Let S be closed, m-convex subset of R d S locally a full ddimensional, with Q the corresponding set of Inc points of S If q is an essential inc point of order k then for some neighborhood U of q Q u is expressible as a union of k or fewer (d2)-dimenslonal manifolds, each containing q For S compact, if to every q E Q there corresponds a k > 0 such that q is an essential inc point of order k then...

A convex variational formulation is proposed to solve multicomponent signal processing problems in Hilbert spaces. The cost function consists of a separable term, in which each component is modeled through its own potential, and of a coupling term, in which constraints on linear transformations of the components are penalized with smooth functionals. An algorithm with guaranteed weak convergenc...

A few Karush-Kuhn-Tucker type of sufficient optimality conditions are given in this paper for nonsmooth continuous-time nonlinear multi-objective optimization problems in the Banach space L∞ [0, T ] of all n-dimensional vector-valued Lebesgue measurable functions which are essentially bounded, using Clarke regularity and generalized convexity. Further, we establish duality theorems for Wolfe an...

Baire category techniques are known to be a powerful tool in the investigation of the convex sets. Their use, which goes back to the fundamental contribution of Klee [17], has permitted to discover several interesting unexpected properties of convex sets (see Gruber [14], Schneider [23], Zamfirescu [25]). A survey of this area of research and additional bibliography can be found in [15, 27]. In...