This paper is concerned with the study of solution existence of variational inequalities and generalized variational inequalities in reflexive Banach spaces with pseudomonotone operators in the sense of H. Brézis. The obtained results covers some preceding results in [4], [11] and [14].

In this paper, we introduce the notion of extended relaxed -monotonicity. We obtain existence solution of the generalized mixed equilibrium problems in reflexive Banach spaces with extended relaxed -monotonicity by using the KKM technique. Our results extend and improve the corresponding results in the existing literature.

By using the technique of factoring weakly compact operators through reflexive Banach spaces we prove that a class of ordinary differential equations with Lipschitz continuous perturbations has a strong solution when the problem is governed by a closed linear operator generating a strongly continuous semigroup of compact operators.

Standard Dutch and German have two reflexive forms: a weak form (zich in Dutch and sich in German) and a strong form (zichzelf in Dutch and sich selbst in German). The choice between the two reflexive forms in Dutch has been explained by the selectional restrictions of the verb, distinguishing between three verb classes: inherently reflexive verbs, accidentally reflexive verbs and transitive ve...

The present paper focuses on the Mandarin Intransitive keflexive Verbs. These verbs, such as zi-sha 'to commit suicide', and zi fen 'to burn oneself, are formed with a reflexive morpheme zi-'self' and a root verb. Take the verb zi-sha 'to commit suicide' for example, the reflexive morpheme contributes the reflexive meaning and the root verb sha 'to kill' contributes the meaning`to kill'; hence,...

We prove that the dual or any quotient of a separable reflexive Banach space with the unconditional tree property has the unconditional tree property. Then we prove that a separable reflexive Banach space with the unconditional tree property embeds into a reflexive Banach space with an unconditional basis. This solves several long standing open problems. In particular, it yields that a quotient...

Most walking assist systems reported are not ready for using in real-world environment; where there are frequent perturbations .Our ultimate goal is to realize artificial reflexes to real-world walking support systems. This goal needs both qualitative and quantitative understanding of human reflexive mechanism. In this study we built a human walking simulator consisting of a Central Pattern Gen...