Inertial projection and contraction algorithms for variational inequalities

In this article, we introduce an inertial projection and contraction algorithm by combining inertial type algorithms with the projection and contraction algorithm for solving a variational inequality in a Hilbert space H. In addition, we propose a modified version of our algorithm to find a common element of the set of solutions of a variational inequality and the set of fixed points of a nonexpansive mapping in H. We establish weak convergence theorems for both proposed algorithms. Finally, we give the numerical experiments to show the efficiency and advantage of the inertial projection and contraction algorithm.     

A new characterization of Möbius transformations by use of Apollonius hexagons

The purpose of this paper is to give a new characterization of Möbius transformations from the standpoint of conformal mappings. To this end a new concept of Apollonius hexagons on the complex plane is used.

     

Contents to Volume 62

Volume Contents

Contents to Volume 62     

A new characteristic of Möbius transformations by use of Apollonius quadrilaterals

The purpose of this paper is to give a new invariant characteristic property of Möbius transformations from the standpoint of conformal mapping. To this end a new concept of ``Apollonius quadrilaterals' is used.

     

The extended Bitsadze-Lavrent’ev-Tricomi boundary value problem

F. G. Tricomi ([5], [6]) originated the theory of boundary of value problems for mixed type equations by establishing the first mixed type equation known asthe Tricomi equation \(y \cdot u_{xx} + u_{yy} = 0\) which is hyperbolic fory<0, elliptic fory>0, and parabolic fory=0 and then observed that this equation could be applied in Aerodynamics and in general in Fluid Dynamics (transonic flows). See: M. Cribario [1], G. Fichera [2], and our doctoral dissertation [4]. Then M. A. Lavrent’ev and A. V. Bitsadze [3] established together a new mixed type boundary value problem for the equation \(\operatorname{sgn} (y) \cdot u_{xx} + u_{yy} = 0\) where sgn (y)=1 fory>0, =?1 fory<0, fory=0, which involved thediscontinuous coefficient K=sgn (y) ofu _xx while in the case of Tricomi equation the corresponding coefficientT=y wascontinuous. In this paper we establish another mixed type boundary value problem forthe extended Bitsadze-Lavrent’ev-Tricomi equation \(L u = \operatorname{sgn} (y) \cdot u_{xx} + \operatorname{sgn} (x) \cdot u_{yy} + r (x,y) \cdot u = f (x,y)\) where both coefficientsK=sgn (y),M=sgn (x) ofu _xx ,u _yy , respectively are discontinous,r=r (x, y) is once continuously differentiable,f=f (x, y) continuous, and then we prove a uniqueness theorem for quasi-regular solutions.     

On homomorphisms between products of median algebras

Homomorphisms of products of median algebras are studied with particular attention to the case when the codomain is a tree. In particular, we show that all mappings from a product \({\mathbf{A_1} \times\ldots\times {\mathbf{A}_{n}}}\) of median algebras to a median algebra \({\mathbf{B}}\) are essentially unary whenever the codomain \({\mathbf{B}}\) is a tree. In view of this result, we also characterize trees as median algebras and semilattices by relaxing the defining conditions of conservative median algebras.     

Synthesis of enantiomerically pure tertiary 1,2-aminoalcohols by the highly diastereoselective reductive ring opening of oxazolidines

A number of enantiomerically pure 1,2-aminoalcohols containing tertiary nitrogen atoms bearing chiral substituents have been prepared by highly diastereoselective reductive ring cleavage of oxazolidines derived from ketones and pseudoephedrine or ephedrine. The ring cleavage occurs with retention of configuration.     

Amino cyclodextrin per-O-methylation: Synthesis of 3-monoamino-permethylated derivatives

A method for the per-O-methylation of amino-cyclodextrins is described. The tert-butyloxycarbonyl protecting group was used for protection of the amino group since it is stable to the alkaline conditions necessary for the permethylation step and can be removed under mildly acidic conditions that leave the cyclodextrin skeleton intact. 3-Monoamino-α-permethylated cyclodextrin and 3-monoamino-β-permethylated cyclodextrin were synthesized based on the above method.     

The space of -additive mappings on semigroups

In this paper, we introduce the concept of -pseudoadditive mappings from a semigroup into a Banach space, and we provide a generalized solution of Ulam's problem for approximately additive mappings.