### A Characterization of Nonlinear ...-Accretive Operators.

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Let C be a closed, bounded, convex subset of a Hilbert space. Let T : C → C be a demicontinuous pseudocontraction. Then T has a fixed point. This is shown by a combination of topological and combinatorial methods.

We establish a connection between generalized accretive operators introduced by F. E. Browder and the theory of quasisymmetric mappings in Banach spaces pioneered by J. Väisälä. The interplay of the two fields allows for geometric proofs of continuity, differentiability, and surjectivity of generalized accretive operators.

We prove existence and uniqueness of solutions for the Dirichlet problem for quasilinear parabolic equations in divergent form for which the energy functional has linear growth.

In this paper we study a nonlinear evolution inclusion of subdifferential type in Hilbert spaces. The perturbation term is Hausdorff continuous in the state variable and has closed but not necessarily convex values. Our result is a stochastic generalization of an existence theorem proved by Kravvaritis and Papageorgiou in [6].

In this paper, following the concepts in [5, 7], we shall establish a convergence result in a uniformly convex Banach space using the Jungck–Mann iteration process introduced by Singh et al [13] and a certain general contractive condition. The authors of [13] established various stability results for a pair of nonself-mappings for both Jungck and Jungck–Mann iteration processes. Our result is a generalization and extension of that of [7] and its corollaries. It is also an improvement on the result...

We prove existence and uniqueness of entropy solutions for the Neumann problem for the quasilinear elliptic equation $u-\mathrm{div}\phantom{\rule{0.166667em}{0ex}}\mathbf{a}(u,Du)=v$, where $v\phantom{\rule{-0.166667em}{0ex}}\in \phantom{\rule{-0.166667em}{0ex}}{L}^{1}$, $\mathbf{a}(z,\xi )={\nabla}_{\xi}f(z,\xi )$, and $f$ is a convex function of $\xi $ with linear growth as $\parallel \xi \parallel \to \infty $, satisfying other additional assumptions. In particular, this class includes the case where $f(z,\xi )=\varphi \left(z\right)\psi \left(\xi \right)$, $\varphi \>0$, $\psi $ being a convex function with linear growth as $\parallel \xi \parallel \to \infty $. In the second part of this work, using Crandall-Ligget’s iteration scheme, this result will permit us to prove existence and uniqueness of entropy solutions for the...

We study in the space of continuous functions defined on [0,T] with values in a real Banach space E the periodic boundary value problem for abstract inclusions of the form ⎧ $x\in S(x\left(0\right),se{l}_{F}\left(x\right))$ ⎨ ⎩ x (T) = x(0), where, $F:[0,T]\times \to {2}^{E}$ is a multivalued map with convex compact values, ⊂ E, $se{l}_{F}$ is the superposition operator generated by F, and S: × L¹([0,T];E) → C([0,T]; ) an abstract operator. As an application, some results are given to the periodic boundary value problem for nonlinear differential inclusions governed by m-accretive...