This work explores the possibility that iterative classes of elliptic equations have both single and coupled positive radial solutions. Our approach is based on using well-known Guo–Krasnoselskii Avery–Henderson fixed-point theorems in a Banach space. Furthermore, we utilize Rus’ theorem metric space, to prove uniqueness solutions for problem. Examples are constructed sake verification.

Let H be a Hilbert space and let C be a closed convex nonempty subset of H and [Formula: see text] a non-self nonexpansive mapping. A map [Formula: see text] defined by [Formula: see text]. Then, for a fixed [Formula: see text] and for [Formula: see text], Krasnoselskii-Mann algorithm is defined by [Formula: see text] where [Formula: see text]. Recently, Colao and Marino (Fixed Point Theory App...

In this paper, we establish sublinear and linear convergence of fixed point iterations generated by averaged operators in a Hilbert space. Our results are achieved under a bounded Hölder regularity assumption which generalizes the well-known notion of bounded linear regularity. As an application of our results, we provide a convergence rate analysis for Krasnoselskii– Mann iterations, the cycli...

In this paper, we show that the modified Mann iteration with errors converges strongly to fixed point for uniformly L-Lipschitzian asymptotically Φ-pseudocontractive mappings in real Banach spaces. Meanwhile, it is proved that the convergence of Mann and Ishikawa iterations is equivalent for uniformly L-Lipschitzian asymptotically Φpseudocontractive mappings in real Banach spaces. Finally, we o...

Suppose that X is a arbitrary real Banach space and T : X → X is a Strongly pseudocontractive mapping. It is proved that certain Mann iterative process with random errors for the fixed point of T is stable(almost stable) with respect to T with(without) Lipschitz condition. And, two related results are obtained that deals with stability(or almost stability) of Mann iterative process for solution...

In this paper, we introduce amodifiedMann iterative process for approximating a common fixedpoint of a finite family of strict pseudo-contractions inHilbert spaces.We establish the strong convergence theorem of the general iteration scheme under some mild conditions. Our results extend and improve the recent ones announced by many others. © 2008 Elsevier Ltd. All rights reserved.