General Relativity (GR) exists in different formulations. They are equivalent pure gravity but generically lead to distinct predictions once matter is included. After a brief overview of various versions GR, we focus on metric-affine gravity, which avoids any assumption about the vanishing curvature, torsion or non-metricity. We use it construct an action scalar field coupled non-minimally grav...

In this article, we present an extension of the controlled rectangular b-metric spaces, so-called metric-like where keep symmetry condition and only change [D(s,r)=0?s=r]to[D(s,r)=0?s=r], which means may have a non-zero self distance; also, D(s,s) is not necessarily less than D(s,r). This new type metric space generalization spaces partial spaces.

introduction: appropriate definition of the distance measure between diffusion tensors has a deep impact on diffusion tensor image (dti) segmentation results. the geodesic metric is the best distance measure since it yields high-quality segmentation results. however, the important problem with the geodesic metric is a high computational cost of the algorithms based on it. the main goal of this ...

Within this manuscript we generalize the two recently obtained results of O. Popescu and G. Stan, regarding F-contractions in complete, ordinary metric space to 0-complete partial metric-like space. As Stan use less conditions than D. Wardovski did his paper from 2012, introduce, with help one our lemmas, a new method proving fixed point theory. Requiring that function F only be strictly increa...