Machine-learning solutions to classification, clustering and matching problems critically depend on the adopted metric, which in the past was selected heuristically. In the last decade, it has been demonstrated that an appropriate metric can be learnt from data, resulting in superior performance as compared with traditional metrics. This has recently stimulated a considerable interest in the to...

Motivated by Nash equilibrium problems on ’curved’ strategy sets, the concept of Nash-Stampacchia equilibrium points is introduced for a finite family of non-smooth functions defined on geodesic convex sets of certain Riemannian manifolds. Characterization, existence, and stability of NashStampacchia equilibria are studied when the strategy sets are compact/noncompact subsets of certain Hadamar...

In this note, we obtain a reverse version of the integral Hardy inequality on metric measure spaces. Moreover, give necessary and sufficient conditions for weighted to be true. The main tool in our proof is continuous Minkowski inequality. addition, present some consequences obtained homogeneous groups, hyperbolic spaces Cartan-Hadamard manifolds.

We derive for a pair of operators on a symplectic space which are adjoints of each other with respect to the symplectic form (that is, they are sympletically adjoint) that, if they are bounded for some scalar product on the symplectic space dominating the symplectic form, then they are bounded with respect to a one-parametric family of scalar products canonically associated with the initially g...

the purpose of this paper is to obtain necessary and suffcient conditionsfor existence approximate fi xed point on geraghty-contraction. in this paper,de nitions of approximate -pair fi xed point for two maps tα , sα and theirdiameters are given in a metric space.

In this paper, we prove some common fixed point results for two self mappingsf and g on S-metric space such that f is a g.w.c.m with respect to g.