On James and von Neumann-Jordan constants and sufficient conditions for the fixed point property

In this paper, we prove that a Banach space X and its dual space X^∗ have uniform normal structure if . The García-Falset coefficient R(X) is estimated by the CNJ(X)-constant and the weak orthogonality coefficient introduced by B. Sims. Finally, we present an affirmative answer to a conjecture by L. Maligranda concerning the relation between the James and CNJ(X)-constants for a Banach space.     

Revising an iterative algorithm for finding a common solution of a system of variational inequalities for two inverse strongly accretive operators

In this paper, we give a short and simple proof of the recent result of Katchang and Kumam (Positivity 15:281–295, 2011). In our proof, we do not assume the uniform convexity of a space.     

Fixed point theorems for contractions of Reich type on a metric space with a graph

In a metric space with a directed graph G, Jachymski (Proc Am Math Soc 1(136):1359–1373, 2008) introduced the concept of Banach G-contraction and proved two fixed point theorems for such mappings. Bojor (Nonlinear Anal 75:3895–3901, 2012) generalized this concept to Reich G-contraction and obtain a fixed point theorem. Note that Bojor’s theorem is established under the additional type of connectedness of G and it does not include Jachymski’s results as a special case. Moreover, there are some mistakes in several corollaries. Some examples and counterexamples are illustrated. It is our purpose to improve Bojor’s theorem and to present two fixed point theorems for Reich G-contractions. Our results are extensions of the two Jachymski’s theorems. Finally, we also discuss some priori error estimates.     

Chitosan-Pectin Composite Gel Spheres: Effect of Some Formulation Variables on Drug Release

Chitosan-pectin composite gel spheres were prepared by ionotropic gelation method. Pectin solution containing indomethacin, a model drug, was extruded into a mixture of chitosan and calcium chloride. The release behavior of indomethacin from composite gel spheres was investigated in-vitro. The influence of factors affecting release behavior, such as type of pectin, molecular weight of chitosan, cross-linking time and release medium, were discussed in this study. Adding chitosan into gelation medium could retard the release of indomethacin from gel spheres. The different type of pectin used demonstrated slightly different drug release profiles. The higher molecular weight of chitosan showed less indomethacin release than the lower one. The increased cross-linking time slowed the drug release from composite gel spheres. The release of indomethacin from composite gel spheres was also dependent on the release medium. The drug release was slower in tris buffer where no phosphate ions which can induce the precipitation of calcium phosphate. The results suggested that the composite gel spheres of pectin and chitosan could be used as a controlled release drug delivery carrier.     

Strong Convergence of the Halpern Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Spaces

Building upon the subgradient extragradient method proposed by Censor et al., we prove the strong convergence of the iterative sequence generated by a modification of this method by means of the Halpern method. We also consider the problem of finding a common element of the solution set of a variational inequality and the fixed-point set of a quasi-nonexpansive mapping with a demiclosedness property.     

The hyperstability of general linear equation via that of Cauchy equation

Aequationes mathematicae - In this paper, we show that the hyperstability of the general linear equation recently proved by Piszczek (Aequationes Math 88:163–168, 2014) is a direct...     

A reconsideration on convergence of three-step iterations for asymptotically nonexpansive mappings

We illustrate that the control conditions of the main convergence theorems of Yao and Noor [Convergence of three-step iterations for asymptotically nonexpansive mappings, Appl. Math. Comput. in press] are incorrect. We also provide new control conditions which are complementary to Nilsrakoo and Saejung’s results [W. Nilsrakoo, S. Saejung, A new three-step fixed point iteration scheme for asymptotically nonexpansive mappings, Appl. Math. Comput. 181 (2006) 1026–1034].     

Convexity conditions and normal structure of Banach spaces

We prove that F-convexity, the property dual to P-convexity of Kottman, implies uniform normal structure. Moreover, in the presence of the WORTH property, normal structure follows from a weaker convexity condition than F-convexity. The latter result improves the known fact that every uniformly nonsquare space with the WORTH property has normal structure.     

On Maingé’s Approach for Hierarchical Optimization Problems

This paper aims at investigating an iterative method for solving a system of variational inequalities with fixed-point set constraints. Our scheme can be regarded as a more general variant of the algorithm proposed by Maingé. Strong convergence results are established in the setting of Hilbert spaces. We propose an alternative analysis that allows us to relax some assumption imposed in his paper for convergence of the considered method. As a complementary result, we show how to adapt these processes to the case when the constraints involve operators belonging to the class of hemi-contractive mappings; this goes beyond the scope of Maingé’s result.