A new strong convergence theorem for equilibrium problems and fixed point problems in Banach spaces.
A nonstandard fixed point result in ...
A Non-standard Version of the Borsuk-Ulam Theorem
E. Pannwitz showed in 1952 that for any n ≥ 2, there exist continuous maps φ:Sⁿ→ Sⁿ and f:Sⁿ→ ℝ² such that f(x) ≠ f(φ(x)) for any x∈ Sⁿ. We prove that, under certain conditions, given continuous maps ψ,φ:X→ X and f:X→ ℝ², although the existence of a point x∈ X such that f(ψ(x)) = f(φ(x)) cannot always be assured, it is possible to establish an interesting relation between the points f(φ ψ(x)), f(φ²(x)) and f(ψ²(x)) when f(φ(x)) ≠ f(ψ(x)) for any x∈ X, and a non-standard version of the Borsuk-Ulam...
A note fixed point theorems of Diaz and Metcalf
A note on asymptotic contractions.
A note on “Common fixed point of multistep noor iteration with errors for a finite family of generalized asymptotically quasi-nonexpansive mappings”.
A note on Picard iterates of nonexpansive mappings
Let X be a Banach space, C a closed subset of X, and T:C → C a nonexpansive mapping. It has recently been shown that if X is reflexive and locally uniformly convex and if the fixed point set F(T) of T has nonempty interior then the Picard iterates of the mapping T always converge to a point of F(T). In this paper it is shown that if T is assumed to be asymptotically regular, this condition can be weakened much further. Finally, some observations are made about the geometric conditions imposed.
A note on strong convergence of a modified Halpern's iteration for nonexpansive mappings.
A Note on the Measure of Solvability
Let X be an infinite-dimensional Banach space. The measure of solvability ν(I) of the identity operator I is equal to 1.
-properness and fixed point theorems for dissipative type maps.
A remark on Rhoades fixed point theorem for non-self mappings.
A remark on the approximate fixed-point property.
A remark on the minimal displacement problem in spaces uniformly rotund in every direction
We give an example of uniformly rotund in every direction space for which the minimal displacement characteristic is maximal.
A remark to the paper “On condensing discrete dynamical systems”
In the paper a new proof of Lemma 11 in the above-mentioned paper is given. Its original proof was based on Theorem 3 which has been shown to be incorrect.
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 shrinking projection method for generalized mixed equilibrium problems, variational inclusion problems and a finite family of quasi-nonexpansive mappings.
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 system of generalized mixed equilibrium problems and fixed point problems for pseudocontractive mappings in Hilbert spaces.
A viscosity approximation method for finding common solutions of variational inclusions, equilibrium problems, and fixed point problems in Hilbert spaces.