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...

Conventional class of weak keys on RC4 stream cipher is defined as a specific case that combinations of the first three bytes of secret key satisfy two relational equations. This paper expands and generalizes the classes of weak keys using generalized relational equations and special classes of the internal state (called predictive state). We derive the probability that generalized classes of w...

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.

In the absolutely continuous case, order statistics, record values and several other models of ordered random variables can be viewed as special cases of generalized order statistics, which enables a unified treatment of their theory. This paper deals with discontinuous generalized order statistics, continuing on the recent work of Tran (2006). Specifically, we show that in general neither re...