One of the generalizations of the Banach Fixed Point Theorem is due to Matkowski, who replaced contractivity by a weaker but still effective property. The aim of this note is to extend the contraction principle in this spirit for such semimetric spaces that are equipped with a natural generalization of the standard triangle inequality. The stability of fixed points is also investigated in this ...

The probabilistic metric space as one of the important generalization of metric space was introduced by K. Menger in 1942. In this paper, we briefly discuss the historical developments of contraction mappings in probabilistic metric space with some fixed point results.

Here, we derive the exact mean and variance of number weakly protected nodes (the that are not leaves at least one their children is a leaf) in binary search trees grown from random permutations. Furthermore, by using contraction method, prove normal limit law for properly normalized version this tree parameter.

In some scientific fields, a scaling is able to modify the topology of an observed object. Our goal in the present work is to introduce a new formalism adapted to the mathematical representation of this kind of phenomenon. To this end, we introduce a new metric structure the galactic spaces which depends on an ordered field extension of R. Moreover, some natural transformations of the category ...

The fixed points theorems for Rhoades-type contraction mapping were investigated by many authors [1, 5, 8, 10, 13, 16, 22] and the more results on this fields can be found in [2, 4, 9, 11, 15, 23]. Hybrid fixed point theory for nonlinear single-valued and multivalued maps is a new development in the domain of contraction-type multivalued theory (see [3, 7, 10, 12, 14, 17, 18, 20] and references...

In [Fuzzy Sets and Systems 27 (1988) 385-389], M. Grabiec in- troduced a notion of completeness for fuzzy metric spaces (in the sense of Kramosil and Michalek) that successfully used to obtain a fuzzy version of Ba- nachs contraction principle. According to the classical case, one can expect that a compact fuzzy metric space be complete in Grabiecs sense. We show here that this is not the case,...

Myosin II motors embedded within the actin cortex generate contractile forces to modulate cell shape in essential behaviors, including polarization, migration, and division. In sarcomeres, myosin II-mediated sliding of antiparallel F-actin is tightly coupled to myofibril contraction. By contrast, cortical F-actin is highly disordered in polarity, orientation, and length. How the disordered natu...