The fixed point index for compact absorbing contractive admissible maps

An index theory is presented for compact (and more generally compact absorbing contractive) Ads (and more generally Ad) maps.     

The existence of two nontrivial solutions via homological local linking for the non-coercive p-Laplacian Neumann problem

In this paper we consider a nonlinear Neumann problem driven by the p-Laplacian and with a Carathéodory right hand side nonlinearity f(z,x). The hypothesis on f(z,x) does not imply the coercivity of the corresponding Euler functional. Using variational arguments and critical groups we show that the problem has at least two nontrivial smooth solutions.     

Common Fixed Point Theory for Multivalued Contractive Maps of Reich Type in Uniform Spaces

This article presents common fixed point theory for multivalued maps defined on complete gauge spaces. Our analysis is elementary and relies only on properties of the generalized Hausdorff pseudometric.     

Nonexistence and Existence of Multiple Positive Solutions for Superlinear Three-point Boundary Value Problems via Index Theory

This paper discusses both the nonexistence of positive solutions for second-order three-point boundary value problems when the nonlinear term f（t, x, y） is superlinear in y at y = 0 and the existence of multiple positive solutions for second-order three-point boundary value problems when the nonlinear term f（t, x,y） is superlinear in x at ＋∞.     

Convergence theorems for semigroup-type families of non-self mappings

Motivated by a paper Chidume and Zegeye [Strong convergence theorems for common fixed points of uniformly L-Lipschitzian pseudocontractive semi-groups, Applicable Analysis, 86 (2007), 353–366], we prove several strong convergence theorems for a family (not necessarily a semigroup) ℱ = {T(t): t ∈ G} of nonexpansive or pseudocontractive non-self mappings in a reflexive strictly convex Banach space with a uniformly Gateaux differentiable norm, where G is an unbounded subset of ℝ⁺. Our results extend and improve the corresponding ones byMatsushita and Takahashi [Strong convergence theorems for nonexpansive nonself-mappings without boundary conditions,Nonlinear Analysis, 68 (2008), 412–419],Morales and Jung [Convergence of paths for pseudo-contractive mappings in Banach spaces, Proceedings of American Mathematical Society, 128 (2000), 3411–3419], Song [Iterative approximation to common fixed points of a countable family of nonexpansive mappings, Applicable Analysis, 86 (2007), 1329–1337], Song and Xu [Strong convergence theorems for nonexpansive semigroup in Banach spaces, Journal of Mathematical Analysis and Applications, 338 (2008), 152–161], Wong, Sahu, and Yao [Solving variational inequalities involving nonexpansive type mappings, Nonlinear Analysis, (2007) doi:10.1016/j.na. 2007.11.025] in the context of a non-semigroup family of non-self mappings.      

Fullerene/cobalt porphyrin hybrid nanosheets with ambipolar charge transporting characteristics

A novel supramolecular nanoarchitecture, comprising C(60)/Co porphyrin nanosheets, was prepared by a simple liquid-liquid interfacial precipitation method and fully characterized by means of optical microscopy, AFM, STEM, TEM, and XRD. It is established that the highly crystalline C(60)/Co porphyrin nanosheets have a simple (1:1) stoichiometry, and when incorporated in bottom-gate, bottom-contact field-effect transistors (FETs), they show ambipolar charge transport characteristics.     

Synthesis and cytotoxicity studies of achiral azaindole‐substituted titanocenes

From the reaction of 1‐methyl‐1 H‐pyr‐rolo[2,3‐b]pyridine ( 1a ),1‐(methoxymethyl)‐1 H‐pyrrolo[2,3‐b]pyridine ( 1b ), 1‐isopropyl‐1 H‐pyrrolo[2,3‐b]pyridine (1c ), and 1‐(4‐methoxybenzyl)‐1 H‐pyrrolo[2,3‐b]pyridine ( 1d ) under Vilsmeier–Haak conditions, the corresponding aldehydes in position 3 ( 2a–2d ) were synthesized. These aldehydes were transformed in the corresponding fulvenes ( 3a–3d ) by the Knoevenagel condensation and treated with Li[BEt₃H] to obtain the corresponding lithiated cyclopentadienide intermediates ( 3′a–3′d ). These intermediates were, finally transmetallated to titanium with TiCl₄ to yield the 7‐azaindol‐3‐yl‐substituted titanocenes bis {[(1‐methyl‐1‐H‐pyrrolo[2,3‐b]pyridin‐3‐yl)methyl] cyclopentadienyl} titanium(IV) dichloride ( 4a ), bis{[(1‐methoxymethyl‐1‐H‐pyrrolo[2,3‐b]pyridin‐3‐yl)methyl]cyclopentadienyl} titanium(IV)dichloride ( 4b ), bis{[(1‐Isopropyl‐1‐H‐pyrrolo[2,3‐b]pyridin‐3‐yl)methyl]cyclopentadienyl} titanium(IV) dichloride ( 4c ), and bis{[(4‐methoxybenzyl‐1‐H‐pyrrolo[2,3‐b]pyridin‐3‐yl)methyl]cyclopentadienyl} titanium(IV) dichloride ( 4d ). All the titanocenes had their cytotoxicity investigated through MTT‐based preliminary in vitro testing on the Caki‐1 cell lines to determinate their IC₅₀ values. Titanocenes 4a–4c were found to have IC₅₀ values of 120 ± 10, 83 ± 13, and 54 ± 12, µM respectively, whereas 4d showed no cytotoxic activity. © 2011 Wiley Periodicals, Inc. Heteroatom Chem 22:148–157, 2011; View this article online at wileyonlinelibrary.com . DOI 10.1002/hc.20668     

Approximations of ternary Jordan homomorphisms and derivations in multi-C ? ternary algebras

Using fixed point methods, we prove the generalized Hyers–Ulam stability of homomorphisms in multi-C ^? ternary algebras and of derivations on multi-C ^? ternary algebras for the additive functional equation $$\sum_{i=1}^{m}f \bigg(mx_i+\sum_{j=1,\ j\ne i}^{m}x_j\bigg)+ f\bigg(\sum_{i=1}^{m}x_i\bigg)= 2f\bigg(\sum_{i=1}^{m}mx_i\bigg) \quad (m\in {\mathbb{N}},\ m\geqq2).$$      

Impulsive boundary value problems for p(t)-Laplacian’s via critical point theory

In this paper we investigate the existence of solutions to impulsive problems with a p(t)-Laplacian and Dirichlet boundary value conditions. We introduce two types of solutions, namely a weak and a classical one which coincide because of the fundamental lemma of the calculus of variations. Firstly we investigate the existence of solution to the linear problem, i.e. a problem with a fixed rigth hand side. Then we use a direct variational method and next a mountain pass approach in order to get the existence of at least one weak solution to the nonlinear problem.     

Carbolithiation of diphenylacetylene as a stereoselective route to (Z)-tamoxifen and related tetrasubstituted olefins

Carbolithiation of diphenylacetylene can be exploited to generate (E)-1-lithio-1,2-diphenylalkyl-1-enes which can be reacted in situ with triisopropylborate to stereoselectively provide (E)-1,2-diphenyl-1-alkylene boronic acids. These tetrasubstituted vinylboronic acids served as versatile intermediates for the generation of tetrasubstituted olefins with retention of stereochemistry. The application of this method for the stereoselective synthesis of (Z)-tamoxifen and related analogues is described.