We introduce the concept of projective suprametrics and provide new part suprametrics in a normed vector space ordered by a cone. We then examine how the convergence of the underlying norm relates to that of the projective and given suprametrics, and we establish sufficient conditions for the completeness of certain subsets. Moreover, we prove a version of Krein-Rutman theorem via a fixed point theorem in suprametric spaces, and study spectral properties of positive linear operators. Furthermore, we show that operator equations involving some concave or convex operators satisfy a Geraghty contraction and therefore have solutions. As an application, we prove a Perron-Frobenius theorem for a tensor eigenvalue problem.
We characterize the boundedness and compactness of generalized integration operators acting between Fock spaces and apply these characterizations to investigate the path-connected components and the singleton of path-connected components of the space of bounded generalized integration operators. Moreover, we describe the essential norm of these operators.
This article considers a second-order difference equation with constant coefficients in its standard form and two different classes of two-point homogeneous boundary conditions. First, we construct the corresponding Green functions and derive some important properties for further analysis. Next, we propose adequate conditions for the existence of solutions to the considered boundary value problems. Finally, we offer two examples to show the applicability of the main results.
In this paper, we establish several new arctangent- and logarithmic-Hardy-Hilbert integral inequalities. The approach combines fundamental principles with refined techniques from the theory of integral inequalities, leading to a range of original results. Complete proofs are presented together with a discussion of their sharpness and potential applications.
This note introduces a \(1\)-parameter of cubic curves naturally associated to the sphere \(S^4\) considered in the unique \(5\)-dimensional irreducible representation space of \(SO(3)\). Eight examples are discussed with the last two being elliptic curves. Also, two conics are defined naturally in our setting by a special basis of the Lie algebra \(sl(3, \mathbb{R})\).
This paper introduces a unified framework for fixed point theorems involving asymptotically regular mappings in \(b\)-metric spaces through the concept of contractive families. We establish a general fixed point theorem that encompasses various existing results, including those of Kannan-type and generalized contractive conditions, as special cases. In particular, we demonstrate that the recent results of Nagac and Tas [1] emerge naturally as special cases of our main theorem through appropriate parameter choices. The main result employs coefficient functions and a general auxiliary function with strengthened continuity conditions, providing flexibility that allows the derivation of numerous particular cases. Several corollaries with complete proofs are presented to demonstrate that our results properly generalize and extend well-known theorems in the literature.
