$C^r$ convergence of Picard’s successive approximations

Improving Convergence Rate in the Method of Successive Approximations*

An application of the method of successive approximations for obtaining the solution of a nonlinear integral equation arising from a two-point boundary value problem is illustrated. In particular, we show sufficient conditions under which the convergence rate of the sequence can be improved.

Double Successive Rough Set Approximations

We examine double successive approximations on a set, which we denote by L2L1, U2U1, U2L1, L2U1 where L1, U1 and L2, U2 are based on generally non-equivalent equivalence relations E1 and E2 respectively, on a finite non-empty set V. We consider the case of these operators being given fully defined on its powerset P(V ). Then, we investigate if we can reconstruct the equivalence relations which ...

Convergence of Successive Approximations for Fuzzy Differential Equations in The Quotient Space of Fuzzy Numbers

In this paper, we study the fuzzy differential equations in the quotient space of fuzzy numbers. We deal with the convergence of successive approximations of the initial value problem of the fuzzy differential equations under the general uniqueness assumption of Perron type utilizing the comparison functions that is rather instructive. We also discuss the approximate solutions and the error est...

Convergence of the Fuzzy Sequence of Successive Approximations to a Fixed Point

In this paper, the existence of the fixed point of fuzzy sequence of successive approximations is proved. For this idea, the   distance is defined and some theorems are proved in detail.

Convergence of the Sequence of Successive Approximations to a Fixed Point