In this paper, we study the Picard-Mann hybrid iteration process to approximate fixed points of Suzuki's generalized nonexpansive mappings. We establish some weak and strong convergence theorems for such mappings in uniformly convex Banach space.

In a preceding note on the linear case [8], we established the following facts for linear T: (a) If X is reflexive and T is asymptotically bounded (i.e. || T\\ ^ M for some constant M and all nèzl), then the Equation (1) has a solution u for a given ƒ if and only if for any specific #o> the sequence of Picard iterates {xn} starting with x0 is bounded in X (see [2]). (b) For a general Banach spa...

This paper investigates the stability of iteration procedures defined by continuous functions acting on self-maps in continuous metric spaces. Some of the obtained results extend the contraction principle to the use of altering-distance functions and extended altering-distance functions, the last ones being piecewise continuous. The conditions for themaps to be contractive for the achievement o...

Let X, d be a complete metric space and T a self-map of X. Let xn 1 f T, xn be some iteration procedure. Suppose that F T , the fixed point set of T , is nonempty and that xn converges to a point q ∈ F T . Let {yn} ⊂ X and define n d yn 1, f T, yn . If lim n 0 implies that limyn q, then the iteration procedure xn 1 f T, xn is said to be T -stable. Without loss of generality, we may assume that ...

The main results of this paper are concerned with the “bad” behavior of the KP-I equation with respect to a Picard iteration scheme applied to the associated integral equation, for data in usual or anisotropic Sobolev spaces. This leads to some kind of ill-posedness of the corresponding Cauchy problem: the flow map cannot be of class C2 in any Sobolev space.

This article is devoted to showing the existence and uniqueness (EU) of a solution with non-Lipschitz coefficients (NLC) fractional Itô-Doob stochastic differential equations driven by countably many Brownian motions (FIDSDECBMs) order ϰ∈(0,1) using Picard iteration technique (PIT) semimartingale local time (SLT).

Cellular automata have been useful artificial models for exploring how relatively simple rules combined with spatial memory can give rise to complex emergent patterns. Moreover, studying the dynamics of how rules emerge under artificial selection for function has recently become a powerful tool for understanding how evolution can innovate within its genetic rule space. However, conventional cel...