Inexact proximal point method for general variational inequalities

In this paper, we suggest and analyze a new inexact proximal point method for solving general variational inequalities, which can be considered as an implicit predictor-corrector method. An easily measurable error term is proposed with further relaxed error bound and an optimal step length is obtained by maximizing the profit-function and is dependent on the previous points. Our results include several known and new techniques for solving variational inequalities and related optimization problems. Results obtained in this paper can be viewed as an important improvement and refinement of the previously known results. Preliminary numerical experiments are included to illustrate the advantage and efficiency of the proposed method.     

On classes of analytic functions defined by convolution with incomplete beta functions

Carlson and Shaffer [SIAM J. Math. Anal. 15 (1984) 737-745] defined a convolution operator L(a,c) on the class A of analytic functions involving an incomplete beta function ?(a,c;z) as L(a,c)f=?(a,c)?f. We use this operator to introduce certain classes of analytic functions in the unit disk and study their properties including some inclusion results, coefficient and radius problems. It is shown that these classes are closed under convolution with convex functions.     

Some algorithms for hemiequilibrium problems

In this paper, we suggest and analyze a class of iterative methods for solving hemiequilibrium problems using the auxiliary principle technique. We prove that the convergence of these new methods either requires partially relaxed strongly monotonicity or pseudomonotonicity, which is a weaker condition than monotonicity. Results obtained in this paper include several new and known results as special cases.     

Finite difference technique for solving obstacle problems

In this paper, we use the variational inequality theory coupled with finite difference technique to obtain an approximate solution for a class of obstacle problems in elasticity, like those describing the equilibrium configuration of an elastic string stretched over an elastic obstacle. The variational inequality formulation is used to discuss the problem of uniqueness and existence of the solution of the obstacle problems.     

Iterative Schemes for Nonconvex Variational Inequalities

In this paper, we suggest and analyze some iterative methods for solving nonconvex variational inequalities using the auxiliary principle technique, the convergence of which requires either only pseudomonotonicity or partially relaxed strong monotonicity. Our proofs of convergence are very simple. As special cases, we obtain earlier results for solving general variational inequalities involving convex sets.     

Parametric Quintic-Spline Approach to the Solution of a System of Fourth-Order Boundary-Value Problems

In this paper, we use parametric quintic splines to derive some consistency relations which are then used to develop a numerical method for computing the solution of a system of fourth-order boundary-value problems associated with obstacle, unilateral, and contact problems. It is known that a class of variational inequalities related to contact problems in elastostatics can be characterized by a sequence of variational inequations, which are solved using some numerical method. Numerical evidence is presented to show the applicability and superiority of the new method over other collocation, finite difference, and spline methods.     

On General Mixed Quasivariational Inequalities

In this paper, we suggest and analyze several iterative methods for solving general mixed quasivariational inequalities by using the technique of updating the solution and the auxiliary principle. It is shown that the convergence of these methods requires either the pseudomonotonicity or the partially relaxed strong monotonicity of the operator. Proofs of convergence is very simple. Our new methods differ from the existing methods for solving various classes of variational inequalities and related optimization problems. Various special cases are also discussed.     

Multivalued general equilibrium problems

In this paper, we use the auxiliary principle technique to suggest some new classes of iterative algorithms for solving multivalued equilibrium problems. The convergence of the proposed methods either requires partially relaxed strongly monotonicity or pseudomonotonicity. As special cases, we obtain a number of known and new results for solving various classes of equilibrium and variational inequality problems. Since multivalued equilibrium problems include equilibrium, variational inequality and complementarity problems as specials cases, our results continue to hold for these problems.     

On interative algorithms for a class of nonlinear variational inequalities

In this paper we use the auxiliary principle technique to suggest and analyze novel and innovative iterative algorithms for a class of nonlinear variational inequalities. Several special cases, which can be obtained from our main results, are also discussed.     

Synthesis,characterization, antiproliferative,and antimicrobial activity of osmium(II) half-sandwich complexes

New osmium(II)-arene complexes [(η⁶-C₆H₆)OsCl(C₅H₄N-2-CH=N-C₆H₅X)](PF₆) (X = p-flouro (1), p-chloro (2), p-methyl (3)) were synthesized by reaction of the corresponding bidentate N,N′-ligands with the osmium-arene precursor [(η⁶-C₆H₆)Os(μ-Cl)Cl]₂ in a 2:1 ratio. These complexes were characterized by UV–Vis, IR, ¹H, ¹³C NMR spectroscopy, and elemental analysis and, for compound 1, a single crystal X-ray structure was also obtained. The complexes were investigated for antiproliferative activity in vitro against MCF-7 (human breast adenocarcinoma), Caco-2 (human epithelial colorectal adenocarcinoma), and HepG2 (human hepatocellular carcinoma) tumor cell lines. To test their selectivity, the non-tumor HEK293 (human embryonic kidney) cell line was used. The compounds were selective toward the tumor cell lines when compared to the known anticancer drug 5-fluorouracil which displayed low selectivity. The compounds were substantially more active against Caco-2 than 5-fluorouracil. They also showed moderate activity against the other two tumor cell lines. In addition, the antimicrobial activity of complex 2 was explored against a panel of antimicrobial-susceptible and -resistant Gram-negative and Gram-positive bacteria. Complex 2 showed anti-mycobacterial activity against Mycobacterium smegmatis and bactericidal activity against drug-resistant Enterococcus faecalis and methicillin-resistant Staphylococcus aureus ATCC 43300.