In this paper we will demonstrate that, in some conditions, the attractor of a countable iterated function system is a parameterized curve. This fact results by generalizing a construction of J. E. Hutchinson [Hut81].

In this paper, we introduce the concept of partial fuzzy metric on a nonempty set $X$ and give the topological structure and some properties of partial fuzzy metric space. Then some fixed point results are provided.

We shall consider periodic problems for ordinary differential equations of the form $$\left\{\begin{array}{c}{x}^{\text{'}}\left(t\right)=f(t,x\left(t\right)),\hfill \\ x\left(0\right)=x\left(a\right),\hfill \end{array}\right.$$ where $f:[0,a]\times R^n\to R^n$ satisfies suitable assumptions. To study the above problem we shall follow an approach based on the topological degree theory. Roughly speaking, if on some ball of $R^n$, the topological degree of, associated to (), multivalued Poincaré operator $P$ turns out to be different from zero, then problem () has solutions. Next by using the multivalued version of the classical Liapunov-Krasnoselskǐ guiding potential...

By means of the Krasnoselskii fixed piont theorem, periodic solutions are found for a neutral type delay differential system of the form $$x^{\text{'}}\left(t\right)+c{x}^{\text{'}}\left(t-\tau \right)=A\left(t,x\left(t\right)\right)x\left(t\right)+f\left(t,x\left(t-r_1\left(t\right)\right),\cdots ,x\left(t-r_k\left(t\right)\right)\right).$$

We establish new existence results for nontrivial solutions of some integral inclusions of Hammerstein type, that are perturbed with an affine functional. In order to use a theory of fixed point index for multivalued mappings, we work in a cone of continuous functions that are positive on a suitable subinterval of $[0,1]$. We also discuss the optimality of some constants that occur in our theory. We improve, complement and extend previous results in the literature.

Let H be a real Hilbert space and T be a maximal monotone operator on H. A well-known algorithm, developed by R. T. Rockafellar [16], for solving the problem (P) ”To find x ∈ H such that 0 ∈ T x” is the proximal point algorithm. Several generalizations have been considered by several authors: introduction of a perturbation, introduction of a variable metric in the perturbed algorithm, introduction of a pseudo-metric in place of the classical regularization, . . . We summarize some of these extensions...

We study a multilinear fixed-point equation in a closed ball of a Banach space where the application is 1-Lipschitzian: existence, uniqueness, approximations, regularity.

We prove that for each linear contraction T : X → X (∥T∥ ≤ 1), the subspace F = {x ∈ X : Tx = x} of fixed points is 1-complemented, where X is a suitable subspace of L¹(E*) and E* is a separable dual space such that the weak and weak* topologies coincide on the unit sphere. We also prove some related fixed point results.

The author applies a generalized Leggett-Williams fixed point theorem to the study of the nonlinear functional differential equation $x^{\text{'}}\left(t\right)=-a(t,x\left(t\right))x\left(t\right)+f(t,x_t)$. Sufficient conditions are established for the existence of multiple positive periodic solutions.

In this paper, by using recent results on fixed point index, we develop a new fixed point theorem of functional type for the sum of two operators $T+S$ where $I-T$ is Lipschitz invertible and $S$ a $k$-set contraction. This fixed point theorem is then used to establish a new result on the existence of positive solutions to a non-autonomous second order difference equation.