Positive kernels, fixed points, and integral equations
نویسندگان
چکیده
منابع مشابه
COLLOCATION METHOD FOR FREDHOLM-VOLTERRA INTEGRAL EQUATIONS WITH WEAKLY KERNELS
In this paper it is shown that the use of uniform meshes leads to optimal convergence rates provided that the analytical solutions of a particular class of Fredholm-Volterra integral equations (FVIEs) are smooth.
متن کاملIntegral Equations with Contrasting Kernels
0 C(t, s)x(s)ds with sharply contrasting kernels typified by C∗(t, s) = ln(e + (t − s)) and D∗(t, s) = [1 + (t − s)]. The kernel assigns a weight to x(s) and these kernels have exactly opposite effects of weighting. Each type is well represented in the literature. Our first project is to show that for a ∈ L[0,∞), then solutions are largely indistinguishable regardless of which kernel is used. T...
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Absbact. It is shown that the eigeovalues and eigenfunctions for the class of "separable" or "semidegenerate" kernels can be determined from the solution of a linear differential equation, which is usually more amenable to machine solution. The theory is extended to solve a simultaneous diagonalization problem for two separable kernels. Finally, some new connections are obtained between Riccati...
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in this paper it is shown that the use of uniform meshes leads to optimal convergence rates provided that the analytical solutions of a particular class of fredholm-volterra integral equations (fvies) are smooth.
متن کاملFixed Points and Cyclic Contraction Mappings under Implicit Relations and Applications to Integral Equations
Inspired by the fact that the discontinuous mappings cannot be (Banach type) contractions and cyclic contractions need not be continuous, and taking into account that there are applications to integral and differential equations based on cyclic contractions, a new type of cyclic contraction mappings satisfying an implicit relation that involves a control function for a map in a metric space is ...
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ژورنال
عنوان ژورنال: Electronic Journal of Qualitative Theory of Differential Equations
سال: 2018
ISSN: 1417-3875
DOI: 10.14232/ejqtde.2018.1.44