相关论文: A reinterpretation of set differential equations a…

This paper introduces the extended set difference, a generalization of the Hukuhara and generalized Hukuhara differences, defined for compact convex sets in $\mathbb{R}^d$. The proposed difference guarantees existence for any pair of such…

In this paper, we establish an analytic framework for studying set-valued backward stochastic differential equations (set-valued BSDE), motivated largely by the current studies of dynamic set-valued risk measures for multi-asset or…

We investigate the initial value problems for non-homogeneous linear differential equations whose solutions are set-valued maps taking values in the space of nonempty compact convex subsets of $\mathbb{R}^2$, denoted by…

In this paper we solve some differential equations in the $D_h$ derivative in Ward's sense. We use a special metric in the formal power series ring $\K[[x]]$. The solutions of that equations are giving in terms of fixed points for certain…

We define and study ordinary differential equations (ODEs) for functions valued in a Banach module $V$ over a finite-dimensional $\Bbbk$-algebra $\mathit{\Lambda}$ by using the tensor of Banach modules. Furthermore, we show that the…

We characterize the solution of a broad class of convex optimization problems that address the reconstruction of a function from a finite number of linear measurements. The underlying hypothesis is that the solution is decomposable as a…

This article gives dual representations for convex integral functionals on the linear space of regular processes. This space turns out to be a Banach space containing many more familiar classes of stochastic processes and its dual can be…

The purpose of this paper is to study certain set-valued integrals in UMD Banach spaces and provide a compatible form of the martingale representation theorem for set-valued martingales. Under specific conditions, these martingales can be…

In this paper we give sharp extension results for convoluted solutions of abstract Cauchy problems in Banach spaces. The main technique is the use of algebraic structure (for usual convolution product $\ast$) of these solutions which are…

In terms of triples of Banach spaces, we define a large class of boundary problems for ordinary differential equations (of arbitrary order) with singular coefficients.

This article introduces an innovative mathematical framework designed to tackle non-linear convex variational problems in reflexive Banach spaces. Our approach employs a versatile technique that can handle a broad range of variational…

In this paper we study different aspects of the representation of weak*-compact convex sets of the bidual $X^{**}$ of a separable Banach space $X$ via a nested sequence of closed convex bounded sets of $X$.

This paper establishes the existence and uniqueness of solutions for rough differential equations driven by reduced rough paths with low regularity, specifically in the roughness regime $\frac{1}{3} < \alpha \leq \frac{1}{2}$. While the…

To a function with values in the power set of a pre-ordered, separated locally convex space a family of scalarizations is given which completely characterizes the original function. A concept of a Legendre-Fenchel conjugate for set-valued…

In this paper, we mainly focus on the set-valued (stochastic) analysis on the space of convex, closed, but possibly unbounded sets, and try to establish a useful theoretical framework for studying the set-valued stochastic differential…

We study an infinite system of ordinary differential equations that models the evolution of coagulating and fragmenting clusters, which we assume to be composed of identical units. Under very mild assumptions on the coefficients we prove…

A topological structure of the solution set to differential inclusions with impulses at variable times is investigated. In order to do that an appropriate Banach space is defined. It is shown that the solution set is an $R_{\delta}$-set.…

The existence of multiple fixed points for the coercive, bilinear, compact forms defined in the cone in the Banach space. Multiple applications to the integral equations derived from BVPs for differential equations are provided.

In the book, I considered differential equations of order $1$ over Banach $D$\Hyph algebra: differential equation solved with respect to the derivative; exact differential equation; linear homogeneous equation. I considered examples of…

In this paper we solve support vector machines in reproducing kernel Banach spaces with reproducing kernels defined on nonsymmetric domains instead of the traditional methods in reproducing kernel Hilbert spaces. Using the orthogonality of…