Results 151 to 160 of about 1,093 (183)

Modified Noor iterations for nonlinear equations in Banach spaces

Applied Mathematics and Computation, 2006
The author proposes and analyzes a three-step iterative scheme for solving nonlinear linear operator equations in Banach spaces. His results can be viewed as an extension of three-step and two-step iterative schemes of Glowinski, Le Tallec, Noor and Ishikawa.
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Iterative solutions of nonlinear equations in smooth banach spaces

Nonlinear Analysis: Theory, Methods & Applications, 1996
This article presents a small survey of results about the solvability and convergence of different iterative schemes for equations \(Tx=f\) with a uniformly continuous and strongly pseudocontractive operator \(T\) which maps a nonempty closed bounded and convex set \(K\) in a real Banach space \(E\) into itself.
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Nonlinear Impulsive Integral Equations in Banach Spaces

1996
The theory of impulsive integral equations is a new branch of integral equations, and it is closely connected with the theory of impulsive differential equations. This chapter is devoted to nonlinear impulsive integral equations in Banach spaces.
Dajun Guo, V. Lakshmikantham, Xinzhi Liu
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Nonlinear integrodifferential equations in a Banach space

2011
Si prova un risultato di esistenza per una classe di equazioni integrodifferenziali del tipo \[ \left[u'(t)+Au(t)\right]\cap\int_{0}^{t}k(t-s)F(s,u(s))ds\neq\textrm{Ø},0\leq t\leq T \] \[ u(0)=u_{0} \] dove A è un operatore m-accretivo su uno spazio di Banach reale x con risolvente (I+$\lambda$a)$^{-1}$ compatto per ogni $\lambda$>0, k:$\left[0,T\right]
Mitidieri, Enzo, Vrabie, Ioan I.
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Nonlinear evolution equations in an arbitrary Banach space

Israel Journal of Mathematics, 1977
This paper proves the existence of an evolution operatorU(t, s)x 0 corresponding to a weak or generalized solution of the differential equation:du (t)/dt +A (t)u(t) ∋ f(t), u(s) =x 0,t ≧ s; the operatorsA(t) are eachm-accretive in a Banach spaceX and, loosely speaking, have an “L1 modulus of continuity ...
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Nonlinear Integro-Differential Equations in Banach Spaces

1996
This chapter is devoted to nonlinear integro-differential equations in Banach spaces including first order equations and second order equations.
Dajun Guo, V. Lakshmikantham, Xinzhi Liu
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GLOBAL EXISTENCE OF SOLUTION TO NONLINEAR INTEGRODIFFERENTIAL EQUATION IN A BANACH SPACE

Acta Mathematica Scientia, 1989
The paper deals with the nonlinear first order integrodifferential equation \(x'=H(t,x,Tx)\) with the initial value \(x(t_ 0)=x_ 0\), where \(x(t)\) belongs to a real Banach space \(E\) and \((Tx)(t)=\int_{t_ 0}^ t K(t,s)x(s)ds\). Under some conditions on \(H\), \(K\) and using a fixed point theorem by \textit{S. J.
Zhuang, Wan, Yu, Hongyi
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On the Existence of Weak Solutions of Nonlinear Integral Equations in Banach Spaces

Mediterranean Journal of Mathematics, 2015
Within the framework of weak continuous functions (with the topology of weak uniform convergence), and for Henstock-Kurzweil-Pettis integrals, the authors obtain conditions for the existence of solutions of a class of nonlinear integral equations which can be seen as nonlinear Fredholm integral equations expressed as a perturbation of linear equations.
Li, Baolin, Gou, Haide
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Method of monotonization of nonlinear equations in Banach spaces

Mathematical Notes of the Academy of Sciences of the USSR, 1988
Let E be a Banach space with a proper cone, A:E\(\to E\) be a linear bounded operator, and F:E\(\to E\) be a continuous operator. The author suggests a method of two-sided successive approximations for the equation \(u=AF(u)\) of the following form \[ u^{n+1}=(I+\lambda A)^{-1}A(F(u^ n)+\lambda u^ n),\quad u^ 0=\sigma^+,\quad u_{n+1}=(I+\lambda A)^{-1 ...
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ITERATIVE SOLUTIONS FOR SYSTEMS OF NONLINEAR OPERATOR EQUATIONS IN BANACH SPACE

Acta Mathematica Scientia, 2003
On a real Banach space with a partial ordering induced by a normal cone, the author considers a system of nonlinear equations of the form (1) \(u = A(u,u), u = B(u,u)\) under a particular set of assumptions for the operators \(A\) and \(B\) that do not require them to be mixed monotone or continuous.
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