In this paper, we propose a new combined scalarization method of multi-objective optimization problems by using the surplus variables and generalized Tchebycheff norm then use it to obtain some equivalent characterizations (weakly, strictly, properly) efficient solutions adjusting range parameters. These results do not need any convexity assumption conditions object...

Keisuke Taniguchi,1 Masaru Shibata,2 and Alessandra Buonanno3,4 1Graduate School of Arts and Sciences, University of Tokyo, Komaba, Meguro, Tokyo, 153-8902, Japan 2Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, 606-8502, Japan 3Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, Potsdam-Golm, 14476, Germany 4Department of Physics, Uni...

We propose a class of higher-derivative gravities that can be viewed as the Gauss-Bonnet extension Starobinsky model. The theory admits Minkowski spacetime vacuum whose linear spectrum consists graviton and massive scalar mode. In addition to usual Schwarzschild black hole, we use numerical analysis establish in some suitable mass range, new holes carrying hair emerge. hole serves "wall" separa...

In a model of spontaneous scalarization neutron stars proposed by Damour and Esposito-Farese, general relativistic branch becomes unstable to trigger tachyonic growth scalar field $\ensuremath{\phi}$ toward scalarized branch. Applying this scenario cosmology, there is fatal instability during inflation matter dominance being incompatible with solar-system constraints on today's value ${\ensurem...

Black holes in scalar-Gauss-Bonnet gravity are prone to scalarization, that is a spontaneous development of scalar hair for strong enough spacetime curvature while the weak field regime theory coincides with general relativity. Since large associated smaller black hole masses, merging can lead dynamical descalarization. This release newly formed case its mass above scalarization threshold. Depe...

We analyze combinatorial optimization problems with ordinal, i.e., non-additive, objective functions that assign categories (like good, medium and bad) rather than cost coefficients to the elements of feasible solutions. review different optimality concepts for ordinal discuss their similarities differences. then focus on two prevalent are shown be equivalent. Our main lies investigation a bije...

In this paper we introduce some contractive conditions of Meir–Keeler type for two mappings, called f -MK -pair mappings and f -CJM-pair (from Ciric, Jachymski, and Matkowski) mappings, in the framework of regular cone metric spaces and we prove theorems which guarantee the existence and uniqueness of common fixed points. We give also a fixed point result for a multivalued mapping that satisfie...

In the presentwork, usingMinkowski functionals in topological vector spaces, we establish the equivalence between some fixed point results in metric and in (topological vector space) cone metric spaces. Thus, a lot of results in the cone metric setting can be directly obtained from their metric counterparts. In particular, a common fixed point theorem for f -quasicontractions is obtained. Our a...

In vector optimization with a variable ordering structure the partial ordering defined by a convex cone is replaced by a whole family of convex cones, one associated with each element of the space. In recent publications it was started to develop a comprehensive theory for these vector optimization problems. Thereby also notions of proper efficiency were generalized to variable ordering structu...