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In this paper, we prove several fixed point theorems on both of normal partially ordered Banach spaces and regular partially ordered Banach spaces by using the normality, regularity, full regularity, and chain -complete property. Then, by…
A nonlinear equation in a Banach space is written as a linear equation with a linear operator depending on the unknown solution. This method, which we call a global linearization method, differs essentially from the local linearization…
A fast algorithm (linear in the degrees of freedom) for the solution of linear variable-coefficient rational-order fractional integral and differential equations is described. The approach is related to the ultraspherical method for…
We consider Riemannian optimization problems with inequality and equality constraints and analyze a class of Riemannian interior point methods for solving them. The algorithm of interest consists of outer and inner iterations. We show that,…
In the paper we offer a functional-discrete method for solving the Cauchy problem for the first order ordinary differential equations (ODEs). This method (FD-method) is in some sense similar to the Adomian Decomposition Method. But it is…
We consider linear bounded operators acting in Banach spaces with a basis, such operators can be represented by an infinite matrix. We prove that for an invertible operator there exists a sequence of invertible finite-dimensional operators…
We show that the augmented primal-dual gradient algorithms can achieve global exponential convergence with partially strongly convex functions. In particular, the objective function only needs to be strongly convex in the subspace…
The main goal of this paper is to show how some monotonicity methods related with the subdifferential of suitable convex functions and its extensions as m-accretive operators in Banach spaces lead to new and unexpected results showing, for…
We study differentiability properties of convex operators defined on a Banach space with values in an $\Lc_p$ space and of their compositions with monotonic convex functionals on this space. We develop new tools for operators enjoying an…
The goal of this work is to serve as a foundation for deep studies of the topology of state, action, and policy spaces in reinforcement learning. By studying these spaces from a mathematical perspective, we expect to gain more insight into…
In this paper, we propose and analyze a fast two-point gradient algorithm for solving nonlinear ill-posed problems, which is based on the sequential subspace optimization method. A complete convergence analysis is provided under the…
We develop an efficient and convergent numerical method for solving the inverse problem of determining the potential of nonlinear hyperbolic equations from lateral Cauchy data. In our numerical method we construct a sequence of linear…
This paper addresses the study and characterizations of variational convexity of extended-real-valued functions on Banach spaces. This notion has been recently introduced by Rockafellar, and its importance has been already realized and…
We study a class of zeroth-order distributed optimization problems, where each agent can control a partial vector and observe a local cost that depends on the joint vector of all agents, and the agents can communicate with each other with…
In the present paper, we consider the semilocal convergence problems of the two-step Newton method for solving nonlinear operator equation in Banach spaces. Under the assumption that the first derivative of the operator satisfies a…
We consider a space-time fractional parabolic problem. Combining a sinc-quadrature based method for discretizing the Riesz-Dunford integral with $hp$-FEM in space yields an exponentially convergent scheme for the initial boundary value…
We study an abstract linear operator equation on a Banach space by using the inverse of the sum of two sectorial operators. We prove that the boundedness of a special type of operator valued $H^\infty$-calculus is sufficient for maximal…
We consider minimizing a sum of non-smooth objective functions with set constraints in a distributed manner. As to this problem, we propose a distributed algorithm with an exponential convergence rate for the first time. By the exact…
In this article, the class of all Dunford-Pettis $ p $-convergent operators and $ p $-Dunford-Pettis relatively compact property on Banach spaces are investigated. Moreover, we give some conditions on Banach spaces $ X $ and $ Y $ such that…
This paper is focused on some properties of paramonotone operators on Banach spaces and their application to certain feasibility problems for convex sets in a Hilbert space and convex systems in the Euclidean space. In particular, it shows…