Finite dimensional locally convex cones were introduced in [3]. In this paper, we give some characterizations for the dual cone of finite dimensional locally convex cones. We prove that the algebraic dual of any finite dimensional cone is finite dimensional. Also, we prove that the symmetric topology induced on a one-dimensional cone by Euclidean convex quasiuniform structure is the discrete topology. We show that any finite dimensional locally convex cone is separated and symmetric complete.
In this study, we associate a category of boundary value problems with non-homogeneous operators. Using critical point theory, we then identify intervals for the control parameters of the problem, ensuring that the operators possess either three critical points or infinitely many critical points. The investigation of these operators will be conducted within the context of the generalized Orlicz-Sobolev function space.
Let 𝒮_u^* denote the class of all analytic functions f in the unit disk 𝔻:={z∈ℂ:|z|<1} , normalized by f(0)=f'(0)-1=0 that satisfies the inequality | zf'(z)/f(z)-1| <1 in 𝔻 . In the present article, we obtain the sharp estimates of Hankel determinants whose entries are coefficients of f∈𝒮_u^* , logarithmic coefficients of f∈𝒮_u^* and coefficients of inverse of f∈𝒮_u^* , respectively. We also obtain, the sharp estimate of the successive coefficients for functions in the class 𝒮_u^* .
In this paper, we prove the Clarkson inequalities for positive functionals in uniformly complete Φ -algebras via a constructive and representation-free approach.
In this paper, we consider the existence of three weak solutions for a class of quasilinear elliptic operators containing the p(· ) -Laplacian and the mean curvature operator with the Steklov boundary condition. The results for the p(· ) -Laplacian are widely known, however, we attempt in this paper to extend the results to a class of quasilinear elliptic operators containing not only the p(· ) -Laplacian but also the mean curvature operator.
