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8 papers · 1 filter
The strong Ekeland variational principle in quasi-pseudometric spaces
S. Cobzaş
Roughly speaking, Ekeland's Variational Principle (EkVP) (J. Math. Anal. Appl. 47 (1974), 324--353) asserts the existence of strict minima of some perturbed versions of lower semic…
Geometry of the proper asymmetric norm
A. B. Németh
There is given the geometric characterization of an asymmetric norm on the real vector space , for which exists an such that , for each . The…
Mutually polar retractions on convex cones
A. B. Németh
Two retractions Q and R on closed convex cones M and respectively N of a Banach space are called mutually polar if Q+R=I and QR=RQ=0. This note investigates the existence of a pair…
Subadditive retractions on cones and asymmetric vector norms
A. B. Németh, S. Z. Németh
Asymmetric vector norms are generalizations of asymmetric norms, where the subadditivity inequality is understood in ordered vector space sense. This relation imposes strong condit…
Ekeland, Takahashi and Caristi principles in quasi-pseudometric spaces
S. Cobzaş
We prove versions of Ekeland, Takahashi and Caristi principles in sequentially right -complete quasi-pseudometric spaces (meaning asymmetric pseudometric spaces), the equivalenc…
A note on an alternative iterative method for nonexpansive mappings
Laurentiu Leustean, Adriana Nicolae
In this note we point out that results on the asymptotic behaviour of an alternative iterative method are corollaries of corresponding results on the well-known Halpern iteration.