this paper consider the   general  forms of $(alpha,beta)$-fuzzyleft ideals (right ideals, bi-ideals, interior ideals) of an orderedsemigroup, where$alpha,betain{in_{gamma},q_{delta},in_{gamma}wedgeq_{delta}, in_{gamma}vee q_{delta}}$ and $alphaneqin_{gamma}wedge q_{delta}$. special attention is paid to$(in_{gamma},ivq)$-left ideals (right ideals, bi-ideals, interiorideals) and some related  pr...

The titles published in this series are listed at the end of this volume. 1 1 2 4 4 4 5 5 6 6 7 9 Multifunctions and Derivatives Particular Locally Lipschitz Functions and Related Definitions Generalized Jacobians of Locally Lipschitz Functions Pseudo-Smoothness and D°f Piecewise Functions NCP Functions 1.4 Definitions of Regularity Definitions of Lipschitz Properties Regularity Definitions Fun...

This paper deals with Lipschitz triangular norms (t-norms). A partial answer to an open problem of Alsina, Frank and Schweizer is given with regard to strict t-norms with smooth additive generators. A new notion of local Lipschitz property for arbitrary t-norms is introduced. Some remarkable examples of non-Lipschitz continuous ones are provided.

Let M be an o-minimal structure over the real closed field R. We prove the definable smoothing of definable Lipschitz continuous functions. In the case of Lipschitz functions of one variable we are even able to preserve the Lipschitz constant.

We characterize intrinsic Lipschitz functions as maps which can be approximated by a sequence of smooth maps, with pointwise convergent intrinsic gradient. We also provide an estimate of the Lipschitz constant of an intrinsic Lipschitz function in terms of the L∞−norm of its intrinsic gradient.

The Lipschitz constant of a finite normal–form game is the maximal change in some player's payoff when a single opponent changes his strategy. We prove that games with small Lipschitz constant admit pure ǫ-equilibria, and pinpoint the maximal Lipschitz constant that is sufficient to imply existence of pure ǫ-equilibrium as a function of the number of players in the game and the number of strate...

‎Let $mathcal{A}$ be a unital Banach algebra‎, ‎$mathcal{M}$ be a left $mathcal{A}$-module‎, ‎and $W$ in $mathcal{Z}(mathcal{A})$ be a left separating point of $mathcal{M}$‎. ‎We show that if $mathcal{M}$ is a unital left $mathcal{A}$-module and $delta$ is a linear mapping from $mathcal{A}$ into $mathcal{M}$‎, ‎then the following four conditions are equivalent‎: ‎(i) $delta$ is a Jordan left de...