Monotone hybrid projection algorithms for an infinitely countable family of Lipschitz generalized asymptotically quasi-nonexpansive mappings.
Moudafi's viscosity approximations with demi-continuous and strong pseudo-contractions for non-expansive semigroups.
Multivalued contraction with parameter
Multivalued pseudo-contractive mappings defined on unbounded sets in Banach spaces
Let be a real Banach space. A multivalued operator from into is said to be pseudo-contractive if for every in , , and all , . Denote by the set . Suppose every bounded closed and convex subset of has the fixed point property with respect to nonexpansive selfmappings. Now if is a Lipschitzian and pseudo-contractive mapping from into the family of closed and bounded subsets of so that the set is bounded for some and some , then has a fixed point in .
New fixed point free nonexpansive maps on weakly compact, convex subsets of L¹[0,1]
We show that every subset of L¹[0,1] that contains the nontrivial intersection of an order interval and finitely many hyperplanes fails to have the fixed point property for nonexpansive mappings.
New hybrid iterative schemes for an infinite family of nonexpansive mappings in Hilbert spaces.
New iteration methods for asymptotically nonexpansive mappings in uniformly smooth real Banach spaces
New iterative approximation methods for a countable family of nonexpansive mappings in Banach spaces.
New iterative scheme for finite families of equilibrium, variational inequality, and fixed point problems in Banach spaces.
New iterative schemes for asymptotically quasi-nonexpansive mappings.
Non-compact perturbations of -accretive operators in general Banach spaces
In this paper we deal with the Cauchy problem for differential inclusions governed by -accretive operators in general Banach spaces. We are interested in finding the sufficient conditions for the existence of integral solutions of the problem , , where is an -accretive operator, and is a continuous, but non-compact perturbation, satisfying some additional conditions.
Nonconvex sets and fixed points
Nonexpansive mappings and convex sequences
Nonexpansive mappings and iterative methods in uniformly convex Banach spaces.
Nonexpansive mappings defined on unbounded domains.
Non-expansive mappings in spaces of continuous functions.
Nonexpansive maps in generalized Orlicz spaces
Nonexpansive retractions in Hilbert spaces
Let H be a Hilbert space and C ⊂ H be closed and convex. The mapping P: H → C known as the nearest point projection is nonexpansive (1-lipschitzian). We observed that, the natural question: "Are there nonexpansive projections Q: H → C other than P?" is neglected in the literature. Also, the answer is not often present in the "folklore" of the Hilbert space theory. We provide here the answer and discuss some facts connected with the subject.
Nonexpansive retracts in Banach spaces
We study various aspects of nonexpansive retracts and retractions in certain Banach and metric spaces, with special emphasis on the compact nonexpansive envelope property.
Non-linear eigenvalue problems and bifurcations for differentiable multivalued maps