Generalized perspectives of functions of several variables

In this paper, we introduce the notion of multivariate generalized perspectives and verify the necessary and sufficient conditions for operator convexity (concavity) of this notion. We also establish the crossing of the multivariate generalized perspective of regular operator mappings under completely positive linear maps and partial traces

Generalized perspectives of functions of several variables

In this paper, we introduce the notion of multivariate generalized perspectives and verify the necessary and sufficient conditions for operator convexity (concavity) of this notion. We also establish the crossing of the multivariate generalized perspective of regular operator mappings under completely positive linear maps and partial traces

Superstability of mm-additive maps on complete non--Archimedean spaces

The stability problem of the functional equation was conjectured by Ulam and was solved by Hyers in the case of additive mapping. Baker et al. investigated the superstability of the functional equation from a vector space to real numbers.In this paper, we exhibit the superstability of $m$-additive maps on complete non--Archimedean spaces via a fixed point method raised by Diaz and Margolis

A Perspective Approach for Characterization of Lieb Concavity Theorem

Lieb’s extension theorem holds for generalized p + q ∈ [0; 1] and Ando convexity theorem holds for q - r > 1. In this paper, we give a complete characterization for concavity or convexity of Lieb well known theorem in the case where p + q ≥ 1 or p+q ≤ 0. We also characterize some auxiliary results including Ando theorem for q-r ≤ 1