We consider linear operators and equations with partial integrals in Banach ideal spaces, spaces of vector functions, continuous functions. study the action, regularity, duality, algebras, Fredholm properties, invertibility, spectral properties such operators. describe principal integrals. show that are essentially different compared to usual integral equations. obtain conditions for alternativ...

We state mean ergodic theorems with rates of approximation for a new class of operator families. Our result provides a unified approach to convergence rates for many particular strongly continuous solution families associated to linear evolution equations such as the abstract Cauchy problem of the first and second order, and integral Volterra equations of convolution type. We discuss in particu...

In this paper, a Jacobi-collocation spectral method is developed for Volterra integral equations of second kind with a weakly singular kernel. We use some function transformation and variable transformations to change the equation into a new Volterra integral equation defined on the standard interval [−1, 1], so that the solution of the new equation possesses better regularity and the Jacobi or...

Annotation Integral equations, as well their solutions, play an important role in the study of various problems science and technology. Of particular interest are Volterra integral equations. In this paper, a regularizing operator is constructed using method M. Lavrentiev for solving class linear equations third kind.

in this paper, we present a numerical method for solving nonlinear fredholm and volterra integral equations of the second kind which is based on the use of haar wavelets and collocation method. we use properties of block pulse functions (bpf) for solving volterra integral equation. numerical examples show efficiency of the method.

in this article the nonlinear mixed volterra-fredholm integral equations are investigated by means of the modied three-dimensional block-pulse functions (m3d-bfs). this method converts the nonlinear mixed volterra-fredholm integral equations into a nonlinear system of algebraic equations. the illustrative   examples are provided to demonstrate the applicability and simplicity of our   scheme.

We analyze admissibility and exactness of observation operators arising in control theory for Volterra integral equations. We give a necessary and sufficient criterion for an unbounded observation operator to map a solution into L2. We then discuss the Hautus Lemma, giving a partial result and an example where it fails.

The ”freezing” method for ordinary differential equations is extended to the Volterra integral equations in a Banach space of the type x(t)− ∫ t 0 K(t, t− s)x(s)ds = f(t) (t ≥ 0), where K(t, s) is an operator valued function ”slowly” varying in the first argument. Besides, sharp explicit stability conditions are derived. Subject Classification: 45M10, 45N05

The first term of the asymptotics of the best constants in Markov-type inequalities for higher derivatives of polynomials is determined in the two cases where the underlying norm is the L norm with Laguerre weight or the L norm with Gegenbauer weight. The coefficient in this term is shown to be the norm of a certain Volterra integral operator which depends on the weight and the order of the der...

in this work, we present a computational method for solving second kindnonlinear fredholm volterra integral equations which is based on the use ofhaar wavelets. these functions together with the collocation method are thenutilized to reduce the fredholm volterra integral equations to the solution ofalgebraic equations. finally, we also give some numerical examples that showsvalidity and applica...