We provide a complete elaboration of the $L^2$-Hilbert space hypocoercivity theorem for degenerate Langevin dynamics with multiplicative noise, studying longtime behaviour strongly continuous contraction semigroup solving abstract Cauchy problem associated backward Kolmogorov operator. Hypocoercivity constant diffusion matrix was proven previously by Dolbeault, Mouhot and Schmeiser in correspon...

Abstract We introduce a large class of contractive mappings, called Suzuki–Berinde type contraction. show that any contraction has fixed point and characterizes the completeness underlying normed space. A theorem for multivalued mappings is also obtained. These results unify, generalize complement various known comparable in literature.

We call (T (t))t≥0 an abstract delay semigroup. This notion is introduced in more detail in Section 2. The semigroup thus obtained is rarely a contraction semigroup. In this paper we will show that under very mild conditions, we may change the inner product on E into an equivalent inner product, such that the delay semigroup becomes a (generalized) contraction semigroup. A contraction semigroup...

Abstract We improve the rational contractive condition and prove common fixed point in dislocated metric spaces. In addition, new generalized contraction has existence of a solution for system integral equations.