[PDF] Top 20 Some extensions of Darbo's theorem and solutions of integral equations of Hammerstein type

... and integral equations were considered by many investigators and some basic results have been obtained [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, ... See full document

... three solutions. We stress that, by expanding the lists in conditions (S  ), (S  ) below, it is possible to state results for four or more positive ... See full document

... 164). Equations of Hammerstein-type also play a crucial role in the theory of optimal control systems and in automation and network theory (see ... See full document

... given integral equation into a system of non-linear equations, which has to be solved with some kind of iterative ...algebraic equations, thus greatly simplifying the ...numerical ... See full document

... above theorem is valid for a specific Green’s ...nonnegative solutions for systems of Hammerstein integral equations has been widely studied; see for example [–] and references ...of ... See full document

... blow-up times not only converge to T (M, τ ), but also converge with the local order of the collocation methods. The numerical threshold blow-up times of (6.1) with β = 2 also converge to the exact one, but the ... See full document

... approximating solutions of equation (.) when A is an accretive-type operator have become a flourishing area of research for nu- merous ...of solutions of the equation when A is of the ... See full document

... point theorem [22] which is a generalization of Darbo’s Fixed Point theorem ...out some successful efforts to solve many functional-integral equations by applying Darbo condition ... See full document

... Many generalizations and extensions of Darbo’s fixed point theorem can be found in the literature (see, for example, [–] and the references therein). Using the BG-measure of noncompactness, Aghajani et al. ... See full document

... We observe that in Theorem 1.1 and Theorem 1.2, the convergence of the Schemes to the solution of the equation u+KF u = 0 is granted by the existence of a constant which is not clear how it is calculated. ... See full document

... is not less that 2β 3/2 α 1/2 = Θ(ρ 1/2 ) as α → 0 + (and, consequently, β → 1 − and ρ → 0 + ). Thus the O( √ ρ ) general bound of Theorem 5.8 cannot be improved even on two-dimensional biased discrete cube. On ... See full document

... Mönch type result for multivalued maps in ordered Banach ...in some sense, a combination of the Banach contraction principle and the Knaster-Tarski fixed point theo- rem in a partially ordered ... See full document

... on some ideas from [], Riemann type problems for Helmholtz equations in Hermitian Clifford analysis are studied in ...knowledge, some boundary value problems for modified Helmholtz ... See full document

... linear integral equations of the second kind based on Adomian’s decomposition method ...the integral equations system was proposed by Rashidinia and Zarebnia ...Fredholm integral ... See full document

... Above it is shown that the integral operator in the right part of (18) is self-adjoint and positively determined. Hence, its eigenvalues are real and nonnegative [9]. From here follows that  cannot be eigenvalue ... See full document

... Remark 4.2 It is well known that the function R(x) given by Riemann is continuous but pointwise differentiable nowhere on [0, 1] (see, e.g.,[14]), then the distributional derivative R (x) in Eq. (16) is neither HK nor ... See full document

... In this paper, we have extended the idea of the modified Taylor-series expansion method from one dimensional Ham- merstein equation to multivariate Hammerstein equation. Then we have applied it to find the ... See full document

... Keeler type. Consequently, we easily obtain extensions of the well-known theorems to the case of dislocated metric spaces or partial metric ...next theorem of Proinov is strongly extended in Section ... See full document

... Gulzar, Bounds for the Zeros and Extremal Properties of Polynomials, Ph.D thesis, Department of Mathematics, University of Kashmir, Srinagar, 2012.. Rahman, On the Location of Z[r] ... See full document

... has a solution provided f is continuous and satisfies a Lipschitz condition by C. Corduneanu [2]. The definition given here generalizes that of Aumann [1] for set- valued mappings. Kaleva [3] discussed the properties of ... See full document