Mir was the seventh and last manned space station to be launched as part of the Soviet space programme, and was the first true modular space station to be launched.
In this paper, we study an interesting generalization of standard metric spaces, b-metric spaces, dislocated metric spaces, and modular spaces due to the recent work of Jleli and Samet.
A sequence ({x_{n}}) in modular space (X_{rho}) is said to be: (t1): ρ-convergent to (xin X_{rho}) if (rho (x_{n}-x rightarrow0) as (n rightarrowinfty); (t2): ρ-Cauchy if (rho(x_{n}-x rightarrow0row0) as (n, mrightarrowinfty).
A surprising observation is that although F6 is a subset of F4, it is actually closer to F5 in "modular" space (distance = 0.18) than to F4 (distance = 0.26), despite the feeding and exploration circuits not having any neuron in common.
The set X_{w}=X_{w}(x_{0})=bigl{ xin X : w_{lambda} x,x_{0} rightarrow 0text{ as } lambda rightarrow infty bigr} is said to be modular space (around (x_{0})).
A pair of individuals is confined to a modular space, with an audiovisual concert of concurrent brain activity.
This example is a typical application of the methods of modular function spaces to the theory of nonlinear integral and differential equations.
Therefore, our results generalize the results of Kozlowski [23], who proved the existence of common fixed points for semigroups of nonexpansive mappings in modular functions spaces, to the pointwise asymptotic semigroups.
The first systematic study of modular spaces is due to Nakano [19].
On the other hand, in 2010, Chistyakov [14] introduced the notion of a modular metric space which is raised in an attempt to avoid some restrictions of the concept of a modular space (for the literature of a modular space, see e.g. [15 21] and references therein).
