Recently, Nemirovski’s analysis indicates that the extragradient method has the O(1/t) convergence rate for variational inequalities with Lipschitz continuous monotone operators. For the same problems, in the last decades, we have developed a class of Fejér monotone projection and contraction methods. Until now, only convergence results are available to these projection and contraction methods,...

Let H be a real Hilbert space, C a nonempty closed convex subset of H , and T : C → C a mapping. Recall that T is nonexpansive if ‖Tx−Ty‖ ≤ ‖x− y‖ for all x, y ∈ C. A point x ∈ C is called a fixed point of T provided Tx = x. Denote by F(T) the set of fixed points of T , that is, F(T) = {x ∈ C : Tx = x}. Recall that a self-mapping f : C → C is a contraction on C, if there exists a constant α∈ (0...

Apoptosis is a critical regulator of homeostasis in the immune system. In this study we demonstrate that memory CD8(+) T cells are more resistant to apoptosis than naive cells. After whole body irradiation of mice, both naive and memory CD8(+) T cells decreased in number, but the reduction in the number of naive cells was 8-fold greater than that in memory CD8(+) T cells. In addition to examini...

In this article, the contraction mapping principle and Liapunov’s method are used to study qualitative properties of nonlinear Volterra equations of the form x(t) = a(t)− ∫ t 0 C(t, s)g(s, x(s)) ds, t ≥ 0. In particular, the existence of bounded solutions and solutions with various L properties are studied under suitable conditions on the functions involved with this equation.

We study the wave equation in exterior of a bounded domain K with dissipative boundary condition $$\partial _{\nu } u - \gamma (x) \partial _t = 0$$ on $$\Gamma $$ and $$\gamma > 0.$$ The solutions are described by contraction semi-group $$V(t) e^{tG}, \, t \ge eigenvalues $$\lambda _k$$ G $$\text{ Re }\,\lambda _k < yield asymptotically disappearing $$u(t, x) e^{\lambda t} f(x)$$ having expone...

Hypoxia-induced pulmonary hypertension (HPH) is characterized by sustained pulmonary vasoconstriction and vascular remodeling, both of which are mediated by pulmonary artery smooth muscle cell (PASMC) contraction and proliferation, respectively. An increase in cytosolic Ca²⁺ concentration ([Ca²⁺]cyt) is a major trigger for pulmonary vasoconstriction and an important stimulus for cell proliferat...

A strong edge coloring of a graph G is proper edges in such that any two distance at most 2 are colored with distinct colors. The chromatic index χs′(G) the smallest integer l admits using K4(t)-minor free does not contain K4(t) as contraction subgraph, where obtained from K4 by subdividing exactly t−4 times. paper shows every maximum degree Δ(G) has χs′(G)≤(t−1)Δ(G) for t∈{5,6,7} which general...

In this paper, we consider the following forced higher-order nonlinear neutral dynamic equation                           1 2 0 , , m k x t p t x t f t x t x t x t q t t t               , , ,  , on time scales. By using Banach contraction principle, we obtain sufficient conditions for the existence of nonoscillatory solutions for general   p t and whi...