H. Khatibzadeh
Department of Mathematics, University of Zanjan, P. O. Box 45195-313, Zanjan, Iran.
[ 1 ] - Non-homogeneous continuous and discrete gradient systems: the quasi-convex case
In this paper, first we study the weak and strong convergence of solutions to the following first order nonhomogeneous gradient system $$begin{cases}-x'(t)=nablaphi(x(t))+f(t), text{a.e. on} (0,infty)\x(0)=x_0in Hend{cases}$$ to a critical point of $phi$, where $phi$ is a $C^1$ quasi-convex function on a real Hilbert space $H$ with ${rm Argmin}phineqvarnothing$ and $fin L^1(0...
[ 2 ] - On the convergence of solutions to a difference inclusion on Hadamard manifolds
The aim of this paper is to study the convergence of solutions of the following second order difference inclusion begin{equation*}begin{cases}exp^{-1}_{u_i}u_{i+1}+theta_i exp^{-1}_{u_i}u_{i-1} in c_iA(u_i),quad igeqslant 1\ u_0=xin M, quad underset{igeqslant 0}{sup} d(u_i,x)
[ 3 ] - An Alexandroff topology on graphs
Let G = (V,E) be a locally finite graph, i.e. a graph in which every vertex has finitely many adjacent vertices. In this paper, we associate a topology to G, called graphic topology of G and we show that it is an Alexandroff topology, i.e. a topology in which intersec- tion of every family of open sets is open. Then we investigate some properties of this topology. Our motivation is to give an e...
[ 4 ] - الگوریتم نقطه پروکسیمال چیست؟
در حوزۀ بهینه سازیِ محدب، الگوریتم های متعددی برای تقریب نقاط بهینۀ یک تابع محدب وجود دارد که یکی از آنها الگوریتم نقطۀ پروکسیمال است. چون این الگوریتم دارای بنیان نظری ژرف و زیبا و قابلیت تعمیم به فضاهای مجرد با کاربردهای متعدد به ویژه در بهینه سازی غیرهموار، مقید و بزرگ-مقیاس است، به طور گسترده ای مطالعه شده است. در این مقاله، هدف ما این است که خواننده را با مفاهیم اساسی که زیربنای این الگوریت...
[ 5 ] - Convexity and Geodesic Metric Spaces
In this paper, we first present a preliminary study on metric segments and geodesics in metric spaces. Then we recall the concept of d-convexity of sets and functions in the sense of Menger and study some properties of d-convex sets and d-convex functions as well as extreme points and faces of d-convex sets in normed spaces. Finally we study the continuity of d-convex functions in geodesic metr...
Co-Authors