Very recently, Ma et al. (Fixed Point Theory Appl. 2014:206, 2014) introduced C∗-algebra-valued metric spaces as a new concept. Also, Ma and Jiang (Fixed Point Theory Appl. 2015:222, 2015), generalizing this concept, introduced C∗-algebra-valued b-metric spaces. In both frameworks, these and other authors proved some fixed point results. We show in this paper that all these results (as well as ...

The paper aims at initiating and exploring the concept of extended metric known as Strong Altering JS-metric, a stronger version JS-metric. interrelation JS-metric with b-metric dislocated has been analyzed some examples have provided. Certain theorems on fixed points for expansive self-mappings in setting complete space also discussed.

In this paper, we first introduce a new notion of the property (M_{C}) to improve and generalize (G_{C}). After that, present two concepts, proximal b-cyclic contraction type second type, on b-metric spaces. Then, obtain best proximity point results for such mappings in frameworks proximally complete spaces by using (M_{C}). Hence, some existing literature. Finally, illustrative interesting exa...

Let B be a fiber bundle with compact fiber F over a compact Riemannian n-manifold M. There is a natural Riemannian metric on the total space B consistent with the metric on M . With respect to that metric, the volume of a rectifiable section σ : M → B is the mass of the image σ(M) as a rectifiable n-current in B. For any homology class of sections of B, there is a mass-minimizing Cartesian curr...

A Yamabe soliton is considered on an almost-contact complex Riemannian manifold (also known as B-metric manifold), which obtained by a contact conformal transformation of the Reeb vector field, its dual 1-form, B-metric, and associated B-metric. case in potential torse-forming field constant length vertical distribution determined studied. In this way, manifolds from one main classes studied ar...