We introduce a class of η-accretive mappings in a real Banach space and show that the η-proximal point mapping for η-m-accretive mapping is Lipschitz continuous. Further, we develop an iterative algorithm for a class of general variational-like inclusions involving ηaccretive mappings in real Banach space, and discuss its convergence criteria. The class of η-accretivemappings includes several i...

We discuss the equilibrium problem for a continuous bifunction over the fixed point set of a firmly nonexpansive mapping. We then present an iterative algorithm, which uses the firmly nonexpansive mapping at each iteration, for solving the problem. The algorithm is quite simple and it does not require monotonicity and Lipschitz-type condition on the equilibrium function. At the end of the paper...

Suppose that $f$ is a $K$-quasiconformal self-mapping of the unit disk $\mathbb{D}$, which satisfies following: $(1)$ biharmonic equation $\Delta(\Delta f)=g$ $(g\in \mathcal{C}(\overline{\mathbb{D}}))$, (2) boundary condition $\Delta f=\varphi$ ($\varphi\in\mathcal{C}(\mathbb{T})$ and $\mathbb{T}$ denotes circle), $(3)$ $f(0)=0$. The purpose this paper to prove Lipschitz continuos, and, furthe...

Fr echet diierentiability of the solution of the heat equation with respect to a nonlinear boundary condition Arnd RR osch Abstract. Consider the heat equation with a nonlinear function in the boundary condition which depends only on the boundary values x of the solution u of the initial-boundary value problem. The function belongs to a set of admissible diierentiable or uniformly Lipschitz con...

We prove that the regular n × n square grid of points in the integer lattice Z2 cannot be recovered from an arbitrary n2-element subset of Z2 via a mapping with prescribed Lipschitz constant (independent of n). This answers negatively a question of Feige from 2002. Our resolution of Feige’s question takes place largely in a continuous setting and is based on some new results for Lipschitz mappi...

We give a sufficient condition for a metric (homology) manifold to be locally bi-Lipschitz equivalent to an open subset in R n. The condition is a Sobolev condition for a measurable coframe of flat 1-forms. In combination with an earlier work of D. Sullivan, our methods also yield an analytic characterization for smoothability of a Lipschitz manifold in terms of a Sobolev regularity for frames ...

We give a sufficient condition for a metric (homology) manifold to be locally bi-Lipschitz equivalent to an open subset in R n. The condition is a Sobolev condition for a measurable coframe of flat 1-forms. In combination with an earlier work of D. Sullivan, our methods also yield an analytic characterization for smoothability of a Lipschitz manifold in terms of a Sobolev regularity for frames ...

We show the existence result of viable solutions to the differential inclusion ẋ(t) ∈ G(x(t)) + F (t, x(t)) x(t) ∈ S on [0, T ], where F : [0, T ] × H → H (T > 0) is a continuous set-valued mapping, G : H → H is a Hausdorff upper semi-continuous set-valued mapping such that G(x) ⊂ ∂g(x), where g : H → R is a regular and locally Lipschitz function and S is a ball, compact subset in a separable H...

The purpose of this paper is to investigate the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality problem for a monotone, Lipschitz continuous mapping. We introduce an extragradient-like approximation method which is based on so-called extragradient method and viscosity approximation method. We establish...

Suppose that X is a arbitrary real Banach space and T : X → X is a Strongly pseudocontractive mapping. It is proved that certain Mann iterative process with random errors for the fixed point of T is stable(almost stable) with respect to T with(without) Lipschitz condition. And, two related results are obtained that deals with stability(or almost stability) of Mann iterative process for solution...