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Let a < c < b real numbers, (B, |·|) a (real or complex) Banach space, H ∈ C([a, b] x [a, c] x B,B), K ∈ C([a,b]² x B,B), g ∈ C([a,b],B), A : C([a,c],B) → C([a,c],B) and B : C([a,b],B) → C([a, b],B). In this paper we study the following functional integral equation, x(t) = ∫ac H(t,s,A(x)(s))ds + ∫at, K(t,s B(x)(s))ds + g(t), t ∈ [a,b]. By a new variant of fibre contraction principle (A. Petrusel, I.A. Rus, M.A. Serban, Some variants of fibre contraction principle and applications: from existence to the convergence of successive approximations, Fixed Point Theory, 22 (2021), no. 2, 795-808) we give existence, uniqueness and convergence of successive approximations results for this equation. In the case of ordered Banach space B, Gronwall-type and comparison-type results are also given. [ABSTRACT FROM AUTHOR]

In this paper we study a system of operatorial equations in terms of some vectorial measures of noncompactness. The basic tools are the cartesian hull of a subset of a cartesian product and some classical fixed point principle. [ABSTRACT FROM AUTHOR]

In this paper we investigate the following problem (see I.A. Rus, Fixed Point Structure Theory, Cluj Univ. Press, Cluj-Napoca, 2006, pp. 193-194): Let X be a set with structure and (X, S(X),M) be a large fixed point structure on X. Let U ∈ S(X). An operator p : U → U is by definition coincidence producing operator on (X, S(X),M) if for each f ∈ M(U) there exists u ∈ U such that f(u) = p(u). The problem is to study the existence and the properties of these class of operators. For the case of topological space with fixed point property with respect to continuous operators, the starting papers are given by W. Holsztynski (Une g'en'eralization du théorème de Brouwer sur les points invariants, Bull. Acad. Pol. Sc., 12(1964), 603-606) and by H. Schirmer (Coincidence producing maps onto trees, Canad. Math. Bull., 10(1967), 417-423) and for the case of metric spaces with fixed point property with respect to nonexpansive operators, by W.A. Kirk (Universal nonexpansive maps, 95-101, in Proc. 8th ICFPTA (2007), Yokohama Publ., 2008). [ABSTRACT FROM AUTHOR]

In this paper we present four types of Ulam stability for ordinary differential equations: Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability. Some examples and counterexamples are 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]