A resolution of Simon's maximal monotonicity problem.
A result on best approximation in -normed spaces
We study best approximation in -normed spaces via a general common fixed point principle. Our results unify and extend some known results of Carbone [ca:pt], Dotson [do:bs], Jungck and Sessa [ju:at], Singh [si:at] and many of others.
A result on segmenting Jungck–Mann iterates
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...
A semilinear equation in
A sequential iteration algorithm with non-monotoneous behaviour in the method of projections onto convex sets
The method of projections onto convex sets to find a point in the intersection of a finite number of closed convex sets in a Euclidean space, may lead to slow convergence of the constructed sequence when that sequence enters some narrow “corridor” between two or more convex sets. A way to leave such corridor consists in taking a big step at different moments during the iteration, because in that way the monotoneous behaviour that is responsible for the slow convergence may be interrupted. In this...
A set of axioms for the degree of a tangent vector field on differentiable manifolds.
A shrinking projection method for generalized mixed equilibrium problems, variational inclusion problems and a finite family of quasi-nonexpansive mappings.
A simple regularization method for the ill-posed evolution equation
The nonhomogeneous backward Cauchy problem , where is a positive self-adjoint unbounded operator which has continuous spectrum and is a given function being given is regularized by the well-posed problem. New error estimates of the regularized solution are obtained. This work extends earlier results by N. Boussetila and by M. Denche and S. Djezzar.
A singular Gierer—Meinhardt system of elliptic equations
A stability theorem for convergence of a Lyapounov function along trajectories of nonexpansive semigroups.
A stochastic version of Fan's best approximation theorem.
A strong convergence in and upper -continuous operators
A strong convergence theorem for a common fixed point of two sequences of strictly pseudocontractive mappings in Hilbert spaces and applications.
A strong convergence theorem for a family of quasi--nonexpansive mappings in a Banach space.
A strongly degenerate quasilinear equation : the elliptic case
We prove existence and uniqueness of entropy solutions for the Neumann problem for the quasilinear elliptic equation , where , , and is a convex function of with linear growth as , satisfying other additional assumptions. In particular, this class includes the case where , , being a convex function with linear growth as . 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...
A study of variational inequalities for set-valued mappings.
A system of generalized mixed equilibrium problems and fixed point problems for pseudocontractive mappings in Hilbert spaces.
A theorem of Borsuk-Ulam type for multifunctions
A theorem of Meir-Keeler type revisited.
A Theorem of the Closed Graph Type.