In this paper we prove a unique common coupled fixed point theorem for two pairs of $w$-compatible mappings in $S_b$-metric spaces satisfying a contrctive type condition. We furnish an example to support our main theorem. We also give a corollary for Junck type maps.

in this paper we study a representation of a fuzzy subgroup $mu$ of a group $g$, as a product of indecomposable fuzzy subgroups called the components of $mu$.  this representation is unique up to the number of components and their isomorphic copies. in the crisp group theory, this is a well-known theorem attributed to remak, krull, and schmidt. we consider the lattice of fuzzy subgroups and som...

in this paper, we introduce the concepts of $2$-isometry, collinearity, $2$%-lipschitz mapping in $2$-fuzzy $2$-normed linear spaces. also, we give anew generalization of the mazur-ulam theorem when $x$ is a $2$-fuzzy $2$%-normed linear space or $im (x)$ is a fuzzy $2$-normed linear space, thatis, the mazur-ulam theorem holds, when the $2$-isometry mapped to a $2$%-fuzzy $2$-normed linear space...

hadamard (or complete $cat(0)$) spaces are complete, non-positive curvature, metric spaces. here, we prove a nonlinear ergodic theorem for continuous non-expansive semigroup in these spaces as well as a strong convergence theorem for the commutative case. our results extend the standard non-linear ergodic theorems for non-expansive maps on real hilbert spaces, to non-expansive maps on had...

We characterize those formulas of MSO monadic second order logic that are safe for bisim ulation formulas de ning binary relations such that any bisimulation is also a bisimulation with respect to these de ned relations Every such formula is equivalent to one constructed from calculus tests atomic actions and the regular operations The proof uses a characterization of completely additive calcul...

When a number of like-minded voters vote strategically and have limited abilities to communicate the under and overshooting may occur when too few or too many of them vote insincerely. In this paper we discuss this phenomenon and define the concept of a safe strategic vote. We prove that for any onto and non-dictatorial social choice rule there exist a profile at which a voter can make a safe s...

Matching is a relation between object types originally designed to support type-safe subclassing with binary methods. In this paper we generalize it to deal with general covariance by allowing eld and method parameter types to change covariantly in matching types. The result is a signiicant increase in the exibility of subclassing. The generalization is in a diierent direction than the recent p...

We prove a general form of ‘free-cut elimination’ for first-order theories in linear logic, yielding normal forms of proofs where cuts are anchored to nonlogical steps. To demonstrate the usefulness of this result, we consider a version of arithmetic in linear logic, based on a previous axiomatisation by Bellantoni and Hofmann. We prove a witnessing theorem for a fragment of this arithmetic via...

In this paper we present an approach towards safe software composition based on aspect-orientation. Aspects enable the systematic addition of code into existing programs but often they also introduce errors. In order to provide safe aspects for software composition we address the verification of the aspect-oriented language paradigm. We construct a basic calculus for aspects with types and prov...

in this note, we aim to present some properties of the space of all weakly fuzzy bounded linear operators, with the bag and samanta’s operator norm on felbin’s-type fuzzy normed spaces. in particular, the completeness of this space is studied. by some counterexamples, it is shown that the inverse mapping theorem and the banach-steinhaus’s theorem, are not valid for this fuzzy setting. also...