@article{Aljawi2026, 
author = {Salma Aljawi and Ahad Hamoud Alotaibi and Silvestru Sever Dragomir and Kais Feki},
title = {New inequalities for the        A  -joint weighted numerical radius with applications},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {7},
pages = {20535-20557},
keywords = {semi-Hilbertian space, A-numerical radius, Euclidean-arithmetic mean numerical radius, Davis-Wielandt radius, operator inequalities, positive operator},
url = {https://www.sciopen.com/article/10.3934/math.2026835},
doi = {10.3934/math.2026835},
abstract = {Let    (      K    ,  ⟨  ⋅  ,  ⋅  ⟩  ) be a complex Hilbert space. Let        A   be a positive (semidefinite) bounded linear operator on        K  . We introduce the Euclidean-arithmetic mean        A  -numerical radius for a pair of        A  -bounded operators    (      U    ,      V    ), defined by        ω                  A            ,      e      ,      ε        (      U    ,      V    )  :=      sup                  η        ∈                  Σ          1                                    A                                                      (              (        1        −        ε        )                  |                ⟨                  U                η        ,        η                  ⟩                                    A                                                            |                                2                          +        ε                  |                ⟨                  V                η        ,        η                  ⟩                                    A                                                            |                                2                              )                      1        2              , where    ε  ∈  [  0  ,  1  ],    ⟨      η    1    ,      η    2        ⟩                  A              =  ⟨      A        η    1    ,      η    2    ⟩ for all        η    1    ,      η    2    ∈      K  , and        Σ    1                  A             denotes the unit        A  -sphere. Furthermore, we define the integral Euclidean numerical radius and present several Hermite-Hadamard-type inequalities. Finally, we provide significant applications of our framework by deriving bounds for the Cartesian decomposition of operators and generalizing the Davis-Wielandt radius to a    p-arithmetic mean context with    p  ≥  1.}
}