We give what appears to be the first explicit, easily computable bound on the transportation cost distance with respect to the weighted Hamming metric. The bound follows from Kantorovich duality and a novel inequality, which amounts to bounding the maximal value of certain linear programs and may be of independent interest. We give two application to concentration of measure for dependent processes and pose some open problems and directions for future work.

This paper studies the existence of solutions for fractional differential inclusions of order $q \in (1,2]$ with four-point nonlocal integral boundary conditions. We consider two cases: (a) the multivalued map in the problem is not necessarily convex valued, (b) the multivalued map consists of non-convex values. A nonlinear alternative of Leray Schauder type coupled with the selection theorem of Bressan and Colombo is employed to deal with the first case, while the second case is based on Wegrzyk's fixed point theorem for generalized contractions.

We construct certain Rajchman measures by using integrability properties of the Fourier and Fourier-Stieltjes transforms. In particular, we state a problem and prove that it is equivalent to the known and still unsolved question posed by R. Salem (Trans. Amer. Math. Soc. 53 (3) (1943), p. 439) whether Fourier-Stieltjes coefficients of the Minkowski question mark function vanish at infinity.

Some Jensen type inequalities for square-convex functions of selfadjoint operators in Hilbert spaces under suitable assumptions for the involved operators are given. Applications for particular cases of interest are also provided.

In this article, we study the existence of mild solutions for the nonlocal Cauchy problem for a class of abstract fractional neutral integro-differential equations with infinite delay. The results are obtained by using the theory of resolvent operators. Finally, an application is given to illustrate the theory.

We consider the Cauchy problem for a semi-linear wave equation with nonlinear mixed damping term and time nonlocal nonlinearity in multi-dimensional space $ \mathbb{R}^{N}$, we prove the local existence and nonexistence of global solutions theorems.

In this paper we derive certain algebraic and ergodicity properties of the Berezin transform defined on $L^2(\mathbb {B}_N, d\eta')$ where $\mathbb {B}_{N}$ is the open unit ball in $\mathbb {C}^N, N\geq 1, N \in \mathbb Z,$ $d\eta'(z)=K_{\mathbb {B}_N}(z, z)d\nu(z)$ is the Mobius invariant measure, $K_{\mathbb {B}_N}$ is the reproducing kernel of the Bergman space $L_a^2(\mathbb {B}_N, d\nu)$ and $d\nu$ is the Lebesgue measure on $\mathbb C^N$, normalized so that $\nu (\mathbb {B}_N)=1$. We establish that the Berezin transform $B$ is a contractive linear operator on each of the spaces $L^p(\mathbb {B}_N, d\eta'(z)), 1\leq p\leq \infty,$ $B^n\to 0$ in norm topology and $B$ is similar to a part of the adjoint of the unilateral shift. As a consequence of these results we also derive certain algebraic and asymptotic properties of the integral operator defined on $L^2[0,1]$ associated with the Berezin transform.

This paper deals with the existence and the stability of solutions of a class of fractional order functional Riemann-Liouville Volterra-Stieltjes partial integral equations. Our results are obtained by using an extension of the Burton-Kirk fixed point theorem in the case of an unbounded domain.

We prove continuity of the Riesz potential operator $R^s: E \mapsto {\mathcal C} H,$ in optimal couples $E, CH$, where $E$ is a rearrangement invariant function space and ${\mathcal C} H$ is the generalized Hölder-Zygmund space generated by a function space $H$.