In this paper, we prove some strong convergence approximation theorems of strongly relatively nonexpansive semi-group in the framework of Banach spaces. Using the concept of duality theorems, we obtain analogue results for strongly generalized nonexpansive semi-group and for semi-group of firmly generalized nonexpansive type. The results presented in this paper improve and extend some correspon...

This paper aim that wish to clearly the generality is not derived from ‘aliquid absrahere’ [abstract from some things] and from only ‘ab aliquibus abstrahere’ [abstract something] (Kant, 1770). In other words, generality isn’t derived from concept itself and from only construction of concepts. In English (German, French, and etc.), term of ‘abstraction’ has dual meanings so ambiguity, but the d...

for Invex Programs via Penalty Functions J. Zhang Institute of Applied Mathematics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China X. X. Huang School of Management, Fudan University, Shanghai 200433, China Abstract. In this paper, we apply the quadratic penalization technique to derive strong Lagrangian duality property for an inequality constrained invex program....

We exhibit a recursive procedure that enables us to construct a maximal union of k chains in a nite partially ordered set P for every positive integer k. As a consequence, we obtain an algorithmic proof of Greene's Duality Theorem on the relations between the cardinalities of maximal unions of chains and antichains in a nite poset. Mathematics Subject Classi cations (2000). 05A17, 06A07, 68Q25,...

We discuss metric, algorithmic and geometric issues related to broadly understood complexity of high dimensional convex sets. The specific topics we bring up include metric entropy and its duality, derandomization of constructions of normed spaces or of convex bodies, and different fundamental questions related to geometric diversity of such bodies, as measured by various isomorphic (as opposed...

Existence analysis of primal and dual evolution mixed variational inclusions is performed on the basis of duality principles, rendering primal and dual solvability equivalence, respectively. Via a fixed-point maximal monotone subdifferential resolvent characterization, corresponding existence results are established under a strong monotonicity condition for the time derivative-elliptic combined...

We study intersection homology with general perversities that assign integers to stratum components with none of the classical constraints of Goresky and MacPherson. We extend Goresky and MacPherson’s axiomatic treatment of Deligne sheaves, and use these to obtain Poincaré and Lefschetz duality results for these general perversities. We also produce versions of both the sheaf-theoretic and the ...

A new class of functions namely, second order (b,F)-convex functions, which is an extension of (b,F)-convex functions and second order F-convex functions, is introduced. Sufficient optimality conditions for proper efficiency and second order mixed type duality theorems for multiobjective nonlinear programming problems are established under the assumptions of second order (b,F)-convexity on the ...

A fundamental problem in spoken language is the duality between the continuous aspects of phonetic performance and the discrete aspects of phonological competence. We study 2 instances of this problem from the phenomenon of voicing neutralization and vowel harmony. In each case, we present a model where the experimentally observed continuous distinctions are linked to the discreteness of phonol...

A fundamental problem in spoken language is the duality between the continuous aspects of phonetic performance and the discrete aspects of phonological competence. We study two instances of this problem from the phenomenon of voicing neutralization and vowel harmony. In each case, we present a model where the experimentally observed continuous distinctions are linked to the discreteness of phon...