We extend Krupnik’s criterion of self-adjointness of the Cauchy singular integral operator to the case of finitely connected domains. The main aim of the paper is to present a new approach for proof of the criterion. Let G+ be a finitely connected domain bounded by the rectifiable curve C = ∂G+, G− = C \ clos G+ and ∞ ∈ G−. Suppose also that w(z), z ∈ C is a nonnegative weight such that w(z) 6≡...

Let A be the class of all analytic functions which are analytic in the open unit disc U = {z : |z| < 1} and Gb = { f ∈ A : ∣∣∣∣ 1 + zf ′′(z)/f ′(z) zf ′(z)/f(z) − 1 ∣∣∣∣ < b, z ∈ U } . In this paper, we derive sufficient conditions for the integral operator Ii γ (f1, ..., fn)(z) =    z ∫ 0 tγ−1 ( f ′ 1(t) )α1 ( f1(t) t )1−α1 ... ( f ′ n(t) )αn ( fn(t) t )1−αn dt    1 γ to be analytic and ...

We propose an extension to the double iteration method, the Multipower Defect Correction method, which is used to refine approximate eigenelements of integral operators. It consists of an inner/outer iteration where, inside a defect correction iteration, p steps of a power iteration are used. The approximate inverse used in the defect correction is built with an approximation to the reduced res...

An exponentially convergent approximation to the solution of a nonlinear first order differential equation with an operator coefficient in Banach space is proposed. The algorithm is based on an equivalent Volterra integral equation including the operator exponential generated by the operator coefficient. The operator exponential is represented by a Dunford-Cauchy integral along a hyperbola enve...

In this paper, we propose a successive approximation method based on fuzzy wavelet like operator to approximate the solution of linear fuzzy Fredholm integral equations of the second kind with arbitrary kernels. We give the convergence conditions and an error estimate. Also, we investigate the numerical stability of the computed values with respect to small perturbations in the first iteration....

The purpose of this paper is to present some coupled fixed point results on a metric space endowed with two $b$-metrics. We shall apply a fixed point theorem for an appropriate operator on the Cartesian product of the given spaces endowed with directed graphs. Data dependence, well-posedness and Ulam-Hyers stability are also studied. The results obtained here will be applied to prove the existe...

planar d-bar integral equation is one of the inverse scattering solution methods for complex problems including inverse conductivity considered in applications such as electrical impedance tomography (eit). recently two different methodologies are considered for the numerical solution of d-bar integrals equation, namely product integrals and multigrid. the first one involves high computational ...

the traditional fuzzy operators, such as t-norms, t-conorms and averaging operators have been used for soil suitability evaluation to aggregate criteria as an overall suitability index. however, such operators do not account for the degree of compensation common to human aggregation criteria, especially in the presence of conflicting criteria. fuzzy integrals are powerful and flexible aggregati...

An exponentially convergent approximation to the solution of a nonlinear first order differential equation with an operator coefficient in Banach space is proposed. The algorithm is based on an equivalent Volterra integral equation including the operator exponential generated by the operator coefficient. The operator exponential is represented by a Dunford-Cauchy integral along a hyperbola enve...

Abstract. A Rota-Baxter operator of weight λ is an abstraction of both the integral operator (when λ = 0) and the summation operator (when λ = 1). We similarly define a differential operator of weight λ that includes both the differential operator (when λ = 0) and the difference operator (when λ = 1). We further consider an algebraic structure with both a differential operator of weight λ and a...