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In this paper we consider the following problems:

Let (X1,→) and (X2, ↬) be two L-spaces, U be a nonempty subset of X1 × X2 such that UX1:= {X2 ∈ X2 | (X1, X2) ∈ U} is nonempty, for each X1 ∈ X1. Let T1: X1 → X1, T2: U → X2 be two operators and T: U → X1 × X2 defined by T(X1,X2):= (T1(X1),T2(X1,X2)). If we suppose that T(U) ⊂ U, FT1 ≠ ∅ and FT2(X1,·) ≠ ∅ for each X1 ∈ X1, the problem is in which additional conditions T is a weakly Picard operator? In this paper we study this problem in the case when the convergence structures on X1 and X2 are defined by metrics. Some applications to the fixed point equations on spaces of continuous functions are also given. [ABSTRACT FROM AUTHOR]

Let (M, d) be a metric space, .... In this paper, we will give sufficient conditions ensuring that a Frum-Ketkov operator is weakly Picard. Some generalized Frum-Ketkov operators are also studied. [ABSTRACT FROM AUTHOR]

In this note, using the weakly Picard operator technique we will present some qualitative results for operators generated by an operator defined on a Cartesian product of a metric space with itself. The work is based on a recent paper of the authors. [ABSTRACT FROM AUTHOR]

Let Ω ⊂ ℝp, p ∈ ℕ* be a nonempty subset and B(Ω) be the Banach lattice of all bounded real functions on Ω, equipped with sup norm. Let X ⊂ B(Ω) be a linear sublattice of B(Ω) and A: X → X be a positive linear operator with constant functions as the fixed point set. In this paper, using the weakly Picard operators techniques, we study the iterates of the operator A: Some relevant examples are also given. [ABSTRACT FROM AUTHOR]

Let X be a Banach lattice. In this paper we give conditions in which an increasing linear operator, A : X → X is weakly Picard operator (see I.A. Rus, Picard operators and applications, Sc. Math. Japonicae, 58(2003), No. 1, 191-219). To do this we introduce the notion of "invariant linear partition of X with respect to A" and we use contraction principle and Maia's fixed point theorem. Some applications are also given. [ABSTRACT FROM AUTHOR]

Let B be a Banach space, α ≤ a < b ≤ β, K ∊ C([α; β]2×B2;B); g ∊ C([α; β];B) and h ∊ C([α; β]; [α; β]). In this paper, using the Picard operator technique, we will study, in C([α; β];B), the following integral equation x(t) = ∫b a K(t; s; x(s); x(h(s))ds; t ∊ [α; β]. [ABSTRACT FROM AUTHOR]