Abstract We study the inverse problem for singular, irreducible, symmetric M -matrices that consists in characterizing those for which the group inverse is again an M -matrix. We solve the problem for a structured class of such matrices arising from star graphs by employing both matrix-theoretic tools and potential theory on networks. Our approach yields explicit criteria for the M -property of the group inverse in terms of conductances and Doob potentials, and provides a constructive procedure to obtain such families of matrices with the desired property.

Abstract In this paper, we set out to explore a class of operators satisfying the condition $$L_2$$ L 2 , and check for their Fejér monotone convergence, and weak convergence. Moreover, qualitative studies related to a stability and data dependence analysis are presented. Meaningful comparisons with other numerical algorithms are provided, from the point of view of the convergence speed or CPU time. Additionally, a polynomiographic study is carried out to visually and quantitatively showcase how efficiently the proposed iterative process works.

Abstract In this paper, we are concerned with a new class of $$\phi $$ ϕ -fractional spaces involving anisotropic $$\overrightarrow{\tau }(\cdot )$$ τ → ( · ) -Laplacian operators, abbreviated as ( $$\phi ,\overrightarrow{\tau }(\cdot )$$ ϕ , τ → ( · ) )-HFDA, for differential equations with a power-like variable reaction term. By utilizing the Mountain Pass Theorem together with Ekeland’s Principle, we proof the existence of precise intervals of positive parameters that admit nontrivial solutions for an eigenvalue problem since $$\tau _{M}^{+}<q^{-}$$ τ M + < q - . Our main results are novel and contribute to the literature on problems involving ( $$\phi ,\overrightarrow{\tau }(\cdot )$$ ϕ , τ → ( · ) )-HFDA. This investigation enhances the understanding of this specific class of problems.