Tamkang Journal of Mathematics

Golden Poisson Geometry : from algebraic structures to Lie algebras ans Poisson manifolds

2025-12-18T05:16:48+00:00

We introduce a unified framework for Golden Poisson Geometry, built around an operator $\varphi$ satisfying the Golden identity $\varphi^2=\varphi+I$. By developing the notions of Golden algebras, Golden Poisson algebras, and Golden Lie algebras, we describe how $\varphi$ governs new compatibility patterns between algebraic operations, Lie brackets, and Poisson tensors. Linear Golden Poisson structures naturally arise on the duals of Golden Lie algebras, revealing Poisson manifolds endowed with intrinsic Fibonacci-type symmetries. Conceptual parallels with the Poisson–Nijenhuis theory of Kosmann-Schwarzbach (1990) show how Golden operators extend classical recursion phenomena. This framework opens new directions in deformation theory and in the geometric study of polynomial identities.

Our main results include the construction of an infinite Golden-Fibonacci hierarchy of compatible Poisson tensors . We establish Golden recurrence relations for hamiltonian vector fields and prove functorial properties showing that the Golden Poisson morphisms transport the entire hierarchical structure. We completely characterize the compatibility conditions between Golden structures and linear Poisson brackets, analyze the associated symplectic foliations, and develop the theory of Golden Poisson morphisms.

On the initial coefficient differences of Ma-Minda starlike functions and bounded turning functions

2026-04-17T08:33:37+00:00

Let $\Phi $ be a univalent function in the unit disk $\mathbb{D}$ and let $\Phi (\mathbb{D})$ be symmetric with respect to the real axis and starlike with respect to $\Phi(0)=1$, also $\Phi ^{\prime }(0)>0$. For the given function $\Phi$, let $\mathcal{S^{\ast }}(\Phi)$ and $\mathcal{R}(\Phi)$ be classes of Ma-Minda starlike functions and bounded turning functions, respectively. In this article, we establish the sharp lower and upper bounds of initial coefficient differences for the functions in $\mathcal{S^{\ast }}(\Phi)$ and $\mathcal{R}(\Phi)$. We also obtain the bounds for the inverse coefficients, logarithmic, and inverse logarithmic coefficients for these classes. All the results we study are sharp.

The Split Feasibility Problems with Multiple Output Sets in real Banach spaces

2026-04-24T04:32:30+00:00

This paper aims to present a new iterative method for solving the split feasibility problem with multiple output sets for generalized demimetric mappings and solution sets of a generalized equilibrium problem in the real Banach spaces. The strong convergence of the sequence generated by our method is proven under certain conditions. We also give a numerical example to support our main result. The results of this paper extend and improve some recent corresponding results announced by many other authors.

A new class of self referred equations with a nonlocal boundary condition

2026-04-23T06:58:13+00:00

We study a nonlinear integro-differential equation with memory and a nonlocal energy constraint. We will use a fixed point approach and prove, via the Schauder fixed point theorem, that under suitable assumptions the problem admits at least one solution. Compared to previous papers, we will work in a more regular function space and impose new structural assumptions.

Characterizations of PR-Slant Warped Submanifolds in Para-Kaehler Spaces via Weingarten Maps

2026-03-10T15:24:46+00:00

This paper investigates $\mathcal{P}\mathcal{R}$-pseudo-slant warped product submanifolds in para-K\"{a}hler manifolds $\bar{F}^{2m}$. First, fundamental properties of $\mathcal{P}\mathcal{R}$-pseudo-slant submanifolds in $\bar{F}^{2m}$ are obtained. Then non-existence and characterization results for $\mathcal{P}\mathcal{R}$-pseudo-slant warped product submanifolds are derived in terms of the Weingarten and endomorphism mappings, including the corresponding slant factor in $\bar{F}^{2m}$. In addition, a numerical example of the warped product $F_{\lambda}\times_{f}F_{\bot}$ in $\bar{F}^{2m}$ is provided to illustrate the results.

Parabolic Frequency on Ricci-Bourguignon flow and Yamabe flow

2025-12-30T05:55:33+00:00

We analyze the evolution of certain parabolic-type energy expressions associated with linear heat-type equations in the setting of compact Riemannian manifolds undergoing the Ricci–Bourguignon and Yamabe flows. By formulating appropriate frequency-type quantities tailored to the underlying geometric dynamics, we demonstrate their monotonic nature under specific curvature assumptions and flow-adapted conditions. This study contributes to the understanding of the interaction between geometric evolution and analytic invariants.