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For each sequence X of finite-dimensional Banach spaces there exists a sequence H of finite connected nweighted graphs with maximum degree 3 such that the following conditions on a Banach space Y are equivalent: (1) Y admits uniformly…
We obtain boundedness for the bilinear spherical maximal function in a range of exponents that includes the Banach triangle and a range of $L^p$ with $p<1$. We also obtain counterexamples that are asymptotically optimal with our positive…
We are concerned with surjectivity of perturbations of maximal monotone operators in non-reflexive Banach spaces. While in a reflexive setting, a classical surjectivity result due to Rockafellar gives a necessary and sufficient condition to…
We characterize non-reflexive Banach spaces by a low-distortion (resp. isometric) embeddability of a certain metric graph up to a renorming. Also we study non-linear sufficient conditions for $\ell_1^n$ being $(1+\varepsilon)$-isomorphic to…
We provide an approach to maximal monotone bifunctions based on the theory of representative functions. Thus we extend to nonreflexive Banach spaces recent results due to A.N. Iusem and, respectively, N. Hadjisavvas and H. Khatibzadeh,…
In this paper, we give sufficient conditions on the spectral radius for a bipartite graph to Hamiltonian and traceable, which expand the results of Lu, Liu and Tian (2012) [10]. Furthermore, we also present tight sufficient conditions on…
In this paper, the sharp maximal theorem is generalized to mixed-norm ball Banach function spaces, which is defined as Definition 2.7. As an application, we give a characterization of BMO via the boundedness of commutators of fractional…
We prove several new sufficient conditions for hamiltonicity and bipancyclicity in balanced bipartite digraphs, in terms of sums of degrees over dominating or dominated pairs of vertices.
We derive a boundary monotonicity formula for a class of biharmonic maps with Dirichlet boundary conditions. A monotonicity formula is crucial in the theory of partial regularity in super-critical dimensions. As a consequence of such a…
In this paper, firstly, we provide some necessary and sufficient conditions for generalized Cayley graphs on abelian groups to be bipartite. Secondly, we deduce several necessary and sufficient conditions for generalized Cayley graphs on…
Necessary and sufficient conditions for Banach space to be(isometrically isomorphic to) a dual space will be given.
Let $X$ be a real reflexive Banach space and $X^*$ be its dual space. Let $G_1$ and $G_2$ be open subsets of $X$ such that $\bar G_2\subset G_1$, $0\in G_2$, and $G_1$ is bounded. Let $L: X\supset D(L)\to X^*$ be a densely defined linear…
We show that a separable real Banach space embeds almost isometrically in a space $Y$ with a shrinking 1-unconditional basis if and only if $\lim_{n \to \infty} \|x^* + x_n^*\| = \lim_{n \to \infty} \|x^* - x_n^*\|$ whenever $x^* \in X^*$,…
In this communication, the co-maximal subgroup graph $\Gamma(G)$ of a finite group $G$ is examined when $G$ is a finite nilpotent group, finite abelian group, dihedral group $D_n$, dicyclic group $Q_{2^n}$, and $p$-group. We derive the…
In this paper, we give the definability of bilinear singular and fractional integral operators on Morrey-Banach space, as well as their commutators and we prove the boundedness of such operators on Morrey-Banach spaces. Moreover, the…
Let $D$ be a strongly connected balanced bipartite directed graph of order $2a\geq 10$ other than a directed cycle. Let $x,y$ be distinct vertices in $D$. $\{x,y\}$ dominates a vertex $z$ if $x\rightarrow z$ and $y\rightarrow z$; in this…
The purpose of this article is to generalize some known characterizations of Banach space properties in terms of graph preclusion. In particular, it is shown that superreflexivity can be characterized by the non-equi-bi-Lipschitz…
Let $G$ be a bipartite graph with bipartition $(X,Y)$. Inspired by a hypergraph problem, we seek an upper bound on the number of disjoint paths needed to cover all the vertices of $X$. We conjecture that a Hall-type sufficient condition…
We investigate the peripheral spectrum of irreducible positive elements of an ordered Banach algebra. In particular, we give conditions under which the peripheral spectrum contains (or coincides with) the cyclic group generated by a root of…
In [{Structural properties and decomposition of linear balanced matrices}, {\it Mathematical Programming}, 55:129--168, 1992], Conforti and Rao conjectured that every balanced bipartite graph contains an edge that is not the unique chord of…