MAXIMAL ELEMENTS OF A FAMILY OF GB-MAJORIZED MAPPINGS IN PRODUCT FC-SPACES AND APPLICATIONS

A new family of GB-majorized mappings from a topological space into a finite continuous topological spaces （in short, FC-space） involving a better admissible set-valued mapping is introduced. Some existence theorems of maximal elements for the family of GB-majorized mappings are proved under noncompact setting of product FCspaces. Some applications to fixed point and system of minimax inequalities are given in product FC-spaces. These theorems improve, unify and generalize many important results in recent literature.     

Near-grazing dynamics in tapping-mode atomic-force microscopy

In tapping-mode atomic-force microscopy, non-linear effects due to large variations in the force field on the probe tip over very small length scales and the intermittency of contact may induce strong dynamical instabilities. In this paper, a discontinuity-mapping-based analysis is employed to investigate the destabilizing effects of low-velocity contact on a lumped-mass model of an oscillating atomic-force-microscope cantilever tip interacting with a typical sample surface. As illustrated using two tip-sample force models, the analysis qualitatively captures the potential loss of stability and disappearance of a low-contact-velocity steady-state response. The quantitative agreement of the predictions of the discontinuity-mapping-based analysis with direct numerical simulations, at least for sufficiently low contact velocity, supports its use in the passive redesign or active control of the tip-sample mechanism for purposes of preventing such a loss of stability.     

On Convergence of Quasi ρ-preserving Locally Related Quasi-nonexpansive Mappings

The concept of quasi-nonexpansive mappings was initiated in Diaz and Metcalf (Bull. Amer. Math. Soc. 73 (1967), 516–519), further it was generalized by Petryshyn and Williamson (Journal of Mathematical Analysis and Applications 43, no. 2 (1973): 459-497). Further investigating the above work, in this article a Banach space with a relation ρ has been considered, the notion of ρ-preserving and quasi ρ-preserving locally related quasi-nonexpansive mappings has been introduced. It has been shown that every ρ-preserving mapping is a quasi ρ-preserving and every nonexpansive mapping is locally related quasi-nonexpansive but converse may not hold. The necessary and sufficient conditions for the convergence of Picard, Mann and Ishikawa iterations of ρ-preserving, quasi ρ-preserving locally related quasi-nonexpansive mappings are presented.     

a-convex convergent alternating series

Teaching in a Mathematics Learning Centre requires special skills and knowledge of the theory of teaching and learning. This paper explores those skills and knowledge then considers how they can be applied to help students attain their full academic potential.     

On functional identities in left ideals of prime rings

In the present paper we describe surjective Lie and Jordan maps onto left ideals of prime noncommutative rings. Further, we describe bijective linear maps of left ideals of centrally closed prime algebras preserving commutativity.     

Noncooperative stochastic games under a n-stage local contraction assumption

We consider a class of noncooperative stochastic games with general state and action spaces and with a state dependent discount factor. The expected time duration between any two stages of the game is not bounded away from zero, so that the usual N-stage contraction assumption, uniform over all admissible strategies, does not hold. We propose milder sufficient regularity conditions, allowing strategies that give rise with probability one to any number of simultaneous stages. We give sufficient conditions for the existence of equilibrium and ∈-equilibrium stationary strategies in the sense of Nash. In the two-player zero-sum case, when an equilibrium strategy exists, the value of the game is the unique fixed point of a specific functional operator and can be computed by dynamic programming.     

Boundary behaviour of the mappings satisfying generalized inverse modular inequalities

We study the geometric properties of the mappings for which generalized inverse modular inequalities hold. We generalize in this way known theorems from the theory of analytic mappings and the theory of quasiregular mappings, like the theorems of Fatou, M. and F. Riesz, Beurling and Lindelöf and their extensions given for quasiregular mappings by Martio, Rickman and Vuorinen.     

涉及复代数超曲面的全纯映射正规族

本文研究了涉及固定超曲面的全纯映照的正规性问题。利用Aladro 和Krantz对全纯映射族正规性的刻画和Shirosahi建立的一系列涉及一些特殊复代数超曲面的Picard 型定理,得到了全纯映射族的一些正规定则。