By using two new algebraic lemmas we obtain Chen’s inequalities for submanifolds of a Riemannian manifold of nearly quasi-constant curvature endowed with a semi-symmetric non-metric connection. Moreover, we correct a result of C. Özgür and A. Mihai’s paper (Chen inequalities for submanifolds of real space forms with a semi-symmetric non-metric connection, Canad. Math. Bull. 55 (2012), 611–622).

In this paper, our aim was making a metric space on hoop algebras, because of that, we introduced the notion valuation maps from F-quasi-valuation map based hoops and related properties them are investigated. By using these notions, quasi-metric space. The continuity operations is studied with topology induced by quasi-valuation. Also, homomorphism investigated that under which condition an map...

We show that the space of subprobability measures, equivalently continuous valuations, on an algebraic (resp., continuous) complete quasi-metric is again and complete, when equipped with Kantorovich-Rubinstein quasi-metrics dKR (unbounded) or dKRa (bounded), themselves asymmetric forms well-known metric. also dKR-Scott dKRa-Scott topologies then coincide weak topology. obtain similar results fo...

We study the coarse geometry of the Teichmüller space of a compact surface in the Teichmüller metric. We show that this admits a ternary operation, natural up to bounded distance, which endows the space with the structure of a coarse median space whose rank is equal to the complexity of the surface. We deduce that Teichmüller space satisfies a coarse quadratic isoperimetric inequality. We descr...

An approach to point-free geometry based on the notion of a quasi-metric is proposed in which the primitives are the regions and a non symmetric distance between regions. The intended models are the bounded regular closed subsets of a metric space together with the Hausdorff excess measure.

We give the generalization of the method of the space-time description of particle creation by a gravitational field for a scalar field with nonconformal coupling to the curvature. The space-time correlation function is obtained for a created pair of the quasi-particles, corresponding to a diagonal form of the instantaneous Hamiltonian. The case of an adiabatic change of the metric of homogeneo...

The complexity (quasi-metric) space has been introduced as a part of the development of a topological foundation for the complexity analysis of algorithms ([12]). Applications of this theory to the complexity analysis of Divide & Conquer algorithms have been discussed in [12]. Here we obtain several quasi-metric properties of the complexity space. The main results obtained are the Smyth-complet...

in the present paper, we introduces the notion of integral type contractive mapping with respect to ordered s-metric space and prove some coupled common fixed point results of integral type contractive mapping in ordered s-metric space. moreover, we give an example to support our main result.