in this paper, an effective and simple numerical method is proposed for solving systems of integral equations using radial basis functions (rbfs). we present an algorithm based on interpolation by radial basis functions including multiquadratics (mqs), using legendre-gauss-lobatto nodes and weights. also a theorem is proved for convergence of the algorithm. some numerical examples are presented...

Part I: Single Variables: Review and extensions. CR equations and analyticity; Cauchy-Goursat theorem and Cauchy integral formula, Louiville’s theorem; Morera’s theorem; maximum modulus principle; Laurent series and singularities; Riemann extension theorem; residues; Schwartz’s lemma; open mapping theorem; analytic continuation and the dilogarithm; linear fractional transformations; spaces of a...

and Applied Analysis 3 Theorem 2.3 Jensen’s inequality 5, Theorem 2.2 . Let a, b ∈ T with a < b, and suppose I ⊂ R is an interval. Assume h ∈ Crd a, b ,R satisfies ∫b a |h t |Δt > 0. If Φ ∈ C I,R is convex and f ∈ Crd a, b , I , then Φ ⎛ ⎝ ∫b a |h t |f t Δt ∫b a |h t |Δt ⎞ ⎠ ≤ ∫b a |h t |Φ ( f t ) Δt ∫b a |h t |Δt . 2.3 In 6 , Özkan et al. proved that Theorem 2.3 is also true if we use the nabl...

We present an existence theorem for monotonic solutions of a quadratic integral equation of Abel type in C[0, 1]. The famous Chandrasekhar’s integral equation is considered as a special case. The concept of measure of noncompactness and a fixed point theorem due to Darbo are the main tools in carrying out our proof.

We prove an existence theorem for a singular quadratic integral equation with supremum. The quadratic integral equation studied below contains as a special case numerous integral equations encountered in the theory of radiative transfer and in the kinetic theory of gases. We show that the singular quadratic integral equations with supremum has a monotonic solution in C[0, 1]. The concept of mea...

This article begins with a review of quantum measure spaces. Quantum forms and indefinite inner-product spaces are then discussed. The main part of the paper introduces a quantum integral and derives some of its properties. The quantum integral’s form for simple functions is characterized and it is shown that the quantum integral generalizes the Lebesgue integral. A bounded, monotone convergenc...

In this paper, we introduce the Denjoy-Pettis integral of set-valued mappings and investigate some properties of the set-valued Denjoy-Pettis integral. Finally we obtain the Dominated Convergence Theorem and Monotone Convergence Theorem for set-valued DenjoyPettis integrable mappings.

Varadhan’s integration theorem, one of the corner stones of large-deviation theory, is generalized to the context of capacities. The theorem appears valid for any integral that obeys four linearity properties. We introduce a collection of integrals that have these properties. Of one of them, known as the Choquet integral, some continuity properties are established as well.

In this paper, we investigate the existence of periodic solution for a class of nonlinear functional integral equation. We prove a fixed point theorem in a Banach algebra. As an application, an existence theorem about periodic solutions to the addressed functional integral equation is presented. In addition, an example is given to illustrate our result.