Some results for uniformly L -Lipschitzian mappings in Banach spaces

AbstractThe purpose of this work is to prove a strong convergence theorem for a pair of uniformly L-Lipschitzian mappings in Banach spaces. The results presented in the work improve and extend some recent results of Chang [S.S. Chang, Some results for asymptotically pseudo-contractive mappings and asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 129 (2001) 845–853], Cho et al [Y.J. Cho, J.I. Kang, H.Y. Zhou, Approximating common fixed points of asymptotically nonexpansive mappings, Bull. Korean Math. Soc. 42 (2005) 661–670], Ofoedu [E.U. Ofoedu, Strong convergence theorem for uniformly L-Lipschitzian asymptotically pseudocontractive mapping in a real Banach space, J. Math. Anal. Appl. 321 (2006) 722–728], Schu [J. Schu, Iterative construction of fixed point of asymptotically nonexpansive mappings, J. Math. Anal. Appl. 158 (1991) 407–413] and Zeng [L.C. Zeng, On the iterative approximation for asymptotically pseudo-contractive mappings in uniformly smooth Banach spaces, Chinese Math. Ann. 26 (2005) 283–290 (in Chinese); L.C. Zeng, On the approximation of fixed points for asymptotically nonexpansive mappings in Banach spaces, Acta Math. Sci. 23 (2003) 31–37 (in Chinese)]

Some results for uniformly L -Lipschitzian mappings in Banach spaces

AbstractThe purpose of this work is to prove a strong convergence theorem for a pair of uniformly L-Lipschitzian mappings in Banach spaces. The results presented in the work improve and extend some recent results of Chang [S.S. Chang, Some results for asymptotically pseudo-contractive mappings and asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 129 (2001) 845–853], Cho et al [Y.J. Cho, J.I. Kang, H.Y. Zhou, Approximating common fixed points of asymptotically nonexpansive mappings, Bull. Korean Math. Soc. 42 (2005) 661–670], Ofoedu [E.U. Ofoedu, Strong convergence theorem for uniformly L-Lipschitzian asymptotically pseudocontractive mapping in a real Banach space, J. Math. Anal. Appl. 321 (2006) 722–728], Schu [J. Schu, Iterative construction of fixed point of asymptotically nonexpansive mappings, J. Math. Anal. Appl. 158 (1991) 407–413] and Zeng [L.C. Zeng, On the iterative approximation for asymptotically pseudo-contractive mappings in uniformly smooth Banach spaces, Chinese Math. Ann. 26 (2005) 283–290 (in Chinese); L.C. Zeng, On the approximation of fixed points for asymptotically nonexpansive mappings in Banach spaces, Acta Math. Sci. 23 (2003) 31–37 (in Chinese)]

Phasing operator for two oscillators in classical field

The origin of Dicke cooperative states was studied by considering two harmonic oscillators driven by a common field of radiation. The origin is assumed for superradiance in a system of molecules where no mutual interactions exist, but all of the molecules encounter the same field of radiation. A phasing operator as Phi(sub Nu) equals D(alpha) + P(sub Nu)D(alpha), where D(alpha) is the displacing operator and P(sub Nu) the projection operator for constant energy Nu for two oscillators, was derived. The eigenstates of the phasing operator Phi are found to show a finite correlation as in the Dicke cooperative states

anti-9,10-Di(1-naphth­yl)anthracene pyridine disolvate

In the title compound, C34H22·2C5H5N, there is a crystallographic inversion center in the middle of the anthracene ring system. The dihedral angle between the mean planes of the anthracene and naphthalene ring systems is 83.96 (4)°. The crystal structure is stabilized by weak inter­molecular C—H⋯N and C—H⋯π inter­actions

Common fixed point theorems and applications

The purpose of this paper is to discuss the existence of common fixed points for mappings in general quasi-metric spaces. As applications, some common fixed point theorems for mappings in probabilistic quasi-metric spaces are given. The results presented in this paper generalize some recent results

Agmatine protects retinal ganglion cells from hypoxia-induced apoptosis in transformed rat retinal ganglion cell line

<p>Abstract</p> <p>Background</p> <p>Agmatine is an endogenous polyamine formed by the decarboxylation of L-arginine. We investigated the protective effects of agmatine against hypoxia-induced apoptosis of immortalized rat retinal ganglion cells (RGC-5). RGC-5 cells were cultured in a closed hypoxic chamber (5% O₂) with or without agmatine. Cell viability was determined by lactate dehydrogenase (LDH) assay and apoptosis was examined by annexin V and caspase-3 assays. Expression and phosphorylation of mitogen-activated protein kinases (MAPKs; JNK, ERK p44/42, and p38) and nuclear factor-kappa B (NF-κB) were investigated by Western immunoblot analysis. The effects of agmatine were compared to those of brain-derived neurotrophic factor (BDNF), a well-known protective neurotrophin for retinal ganglion cells.</p> <p>Results</p> <p>After 48 hours of hypoxic culture, the LDH assay showed 52.3% cell loss, which was reduced to 25.6% and 30.1% when agmatine and BDNF were administered, respectively. This observed cell loss was due to apoptotic cell death, as established by annexin V and caspase-3 assays. Although total expression of MAPKs and NF-κB was not influenced by hypoxic injury, phosphorylation of these two proteins was increased. Agmatine reduced phosphorylation of JNK and NF-κB, while BDNF suppressed phosphorylation of ERK and p38.</p> <p>Conclusion</p> <p>Our results show that agmatine has neuroprotective effects against hypoxia-induced retinal ganglion cell damage in RGC-5 cells and that its effects may act through the JNK and NF-κB signaling pathways. Our data suggest that agmatine may lead to a novel therapeutic strategy to reduce retinal ganglion cell injury related to hypoxia.</p