Convergence and stability theorems for the Picard-Mann hybrid iterative scheme for a general class of contractive-like operators

In this paper we use the general class of contractive-like operators introduced by Bosede and Rhoades (J. Adv. Math. Stud. 3(2):1-3, 2010) to prove strong convergence and stability results for Picard-Mann hybrid iterative schemes considered in a real normed linear space. We establish the strong convergence and stability of the Picard iterative scheme as a corollary. Our results generalize and improve a multitude of results in the literature, including the recent results of Chidume (Fixed Point Theory Appl. 2014:233, 2014)

On -Stability of Picard Iteration in Cone Metric Spaces

The aim of this work is to investigate the T-stability of Picard's iteration procedures in cone metric spaces and give an application

Comments on the Rate of Convergence between Mann and Ishikawa Iterations Applied to Zamfirescu Operators

In the work of Babu and Vara Prasad (2006), the claim is made that Mann iteration converges faster than Ishikawa iteration when applied to Zamfirescu operators. We provide an example to demonstrate that this claim is false

-Stability of Picard Iteration in Metric Spaces

We establish a general result for the stability of Picard's iteration. Several theorems in the literature are obtained as special cases

Size of Convergence Domains for Generalized Hausdorff Prime Matrices

We show that there exit E-J generalized Hausdorff matrices and unbounded sequences x such that each matrix has convergence domain c circle plus x

Property in -Metric Spaces

We prove two general fixed theorems for maps in G-metric spaces and then show that these maps satisfy property P

Lipidomics Reveals Early Metabolic Changes in Subjects with Schizophrenia: Effects of Atypical Antipsychotics

There is a critical need for mapping early metabolic changes in schizophrenia to capture failures in regulation of biochemical pathways and networks. This information could provide valuable insights about disease mechanisms, trajectory of disease progression, and diagnostic biomarkers. We used a lipidomics platform to measure individual lipid species in 20 drug-naïve patients with a first episode of schizophrenia (FE group), 20 patients with chronic schizophrenia that had not adhered to prescribed medications (RE group), and 29 race-matched control subjects without schizophrenia. Lipid metabolic profiles were evaluated and compared between study groups and within groups before and after treatment with atypical antipsychotics, risperidone and aripiprazole. Finally, we mapped lipid profiles to n3 and n6 fatty acid synthesis pathways to elucidate which enzymes might be affected by disease and treatment. Compared to controls, the FE group showed significant down-regulation of several n3 polyunsaturated fatty acids (PUFAs), including 20:5n3, 22:5n3, and 22:6n3 within the phosphatidylcholine and phosphatidylethanolamine lipid classes. Differences between FE and controls were only observed in the n3 class PUFAs; no differences where noted in n6 class PUFAs. The RE group was not significantly different from controls, although some compositional differences within PUFAs were noted. Drug treatment was able to correct the aberrant PUFA levels noted in FE patients, but changes in re patients were not corrective. Treatment caused increases in both n3 and n6 class lipids. These results supported the hypothesis that phospholipid n3 fatty acid deficits are present early in the course of schizophrenia and tend not to persist throughout its course. These changes in lipid metabolism could indicate a metabolic vulnerability in patients with schizophrenia that occurs early in development of the disease. © 2013 McEvoy et al