Abstract In this paper, we study some properties of generalized Morrey spaces ℳ p , ϕ ( ℝ n ) {\mathcal{M}^{p,\phi}(\mathbb{R}^{n})} . Multiplication operators M u {M_{u}} (which are a class of operators that generalize the notion of operator given by a diagonal matrix) defined on such spaces are also studied. In particular, we obtain results about M u {M_{u}} (e.g., when it is an isometry, its boundedness, etc.). It is shown that the multiplication operator is a self-adjoint operator. Finally, its compactness is also characterized.
Abstract In this paper, we introduce the multiplicative generalized 𝑘-fractional conformable (MK-FCI) left and right integrals and investigate their fundamental properties, including integrability, boundedness, continuity, and the semigroup property. We then establish Hermite–Hadamard (HH) inequalities for these integrals, and further derive midpoint and trapezoidal inequalities as consequences of the obtained Hermite–Hadamard results. We also show how these new inequalities generalize and connect to existing results for multiplicative generalized 𝑘-fractional conformable integrals and classical multiplicative integrals through particular cases. Furthermore, we present novel Hermite–Hadamard, midpoint, and trapezoidal-type inequalities specifically tailored to the MK-FCI framework.
Abstract In this paper, we prove in a first step for a smooth and elliptic anisotropy existence of an expanding regular network under anisotropic curvature flow with initial value given by three different half-lines starting in the same point. To achieve this, we adapt an analogous result from [O. C. Schnürer and F. Schulze, Self-similarly expanding networks to curve shortening flow, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 6 (2007), 4, 511–528] in the isotropic case. In a second step, we extend the existence result with similar methods to the situation where the initial value consists of four different half-lines starting from the same point.
Abstract In this paper, we investigate three systems of quadratic trinomial functional equations, focusing on the existence and specific forms of finite-order transcendental entire solutions. Two systems, one formulated in C n \mathbb{C}^{n} with n ∈ N n\in\mathbb{N} and the other in C 2 \mathbb{C}^{2} , generalize and extend recent results from [Z. Tai, J. Long and X. Xiang, On entire solutions for several systems of quadratic trinomial Fermat type functional equations in C 2 \mathbb{C}^{2} , Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 118 (2024), 4, Paper No. 156]. To illustrate the validity and applicability of our findings, we provide concrete examples.
In the current investigation, we introduce a novel multimixed additive-quartic mapping as a system of mixed additive and quartic functional equations. Then we represent and characterize this system of functional equations as a single equation. We find some relations between this new definition and multi-additive and multi-quartic mappings by using linear and quartic conditions. Moreover, we show that each multimixed additive-quartic mapping can be reduced into either multi-additive or multi-quartic mapping. Furthermore, we prove the Hyers-Ulam stability of multimixed additive-quartic functional equations in the content of quasi-beta-2-Banach spaces. Eventually, we provide some known stability outcomes when the controller bound changes.
