In this paper, we prove the ∆-convergence theorems of the cyclic algorithm and the new multi-step iteration for k-strictly pseudo-contractive mappings and give also the strong convergence theorem of the modified Halpern’s iteration for these mappings in a CAT (0) space. Our results extend and improve the corresponding recent results announced by many authors in the literature. Key–Words: CAT (0...

We show that the range of a contractive projection on a Lebesgue-Bochner space of Hilbert valued functions Lp(H) is isometric to a p-direct sum of Hilbertvalued Lp-spaces. We explicit the structure of contractive projections. As a consequence for every 1 < p < ∞ the class Cp of p-direct sums of Hilbertvalued Lp-spaces is axiomatizable (in the class of all Banach spaces).

In this note, we introduce some contractive conditions which complete the corresponding contractive conditions appeared in references [1]-[11]. By these conditions, we prove that twenty-two contractive conditions are equivalent. Then we use these conditions to get some common fixed point theorems for noncompatible maps and some weakly compatible mappings. There are a number of papers dealing wi...

Let A d be the complex polynomial ring in d variables. A contractive A d-module is Hilbert space H equipped with an A d action such that for any ξ 1 , ξ 2 ,. Such objects have been shown to be useful for modeling d-tuples of mutually commuting operators acting on a Hilbert space. An example is given by H 2 d , which is the Hilbert space of holomorphic functions on B d = {z ∈ C d : |z| ≤ 1} gene...

We propose a new stability constraint for contractive receding horizon control (RHC), which was inspired by a non-monotone line search rule for optimization algorithms. Previously proposed stability constraints for contractive RHC can be seen as special cases of our new constraint. The new stability constraint guarantees asymptotic stability, but it does not ensure the monotone decrease of the ...

The aim of this paper is to present some coincidence and common fixed point results for generalized (ψ, φ)-contractive mappings using partially weakly G-α-admissibility in the setup of G-metric space. As an application of our results, periodic points of weakly contractive mappings are obtained. We also derive certain new coincidence point and common fixed point theorems in partially ordered G-m...

Very recently, Agarwal et al. (Fixed Point Theory Appl. 2012:40, 2012) initiated the study of fixed point theorems for mappings satisfying cyclical generalized contractive conditions in complete partial metric spaces. In the present paper, we study some fixed point theorems for a mapping satisfying a cyclical generalized contractive condition based on a pair of altering distance functions in co...

The purpose of this paper is to prove end-point theorems for multivalued mappings satisfying comparatively a more general contractive condition in ordered complete metric spaces. Afterwards, we extend the results of previous sections and prove common end-point results for a pair of T-weakly isotone increasing multivalued mappings in the underlying spaces. Finally, we present common end point fo...

In this paper, we consider, discuss and complement fixed points results for mappings satisfying cyclical contractive conditions established by W. A. Kirk et al. [W. A. Kirk, P. S. Srinivasan, P. Veeramani, Fixed points for mappings satisfying cyclical contractive conditions, Fixed Point Theory, Volume 4, No. 1, 2003, 79-89]. By using our new Lemma we get much shorter and nicer proofs of some re...

‎in this paper we study the existence of fixed points for mappings defined on complete metric spaces‎, ‎satisfying a general contractive inequality depending on two additional mappings‎.