Approximate Efficient Solutions of the Vector Optimization Problem on Hadamard Manifolds via Vector Variational Inequalities

This article has two objectives. Firstly, we use the vector variational-like inequalities problems to achieve local approximate (weakly) efficient solutions of the vector optimization problem within the novel field of the Hadamard manifolds. Previously, we introduced the concepts of generalized approximate geodesic convex functions and illustrated them with examples. We see the minimum requirements under which critical points, solutions of Stampacchia, and Minty weak variational-like inequalities and local approximate weakly efficient solutions can be identified, extending previous results from the literature for linear Euclidean spaces. Secondly, we show an economical application, again using solutions of the variational problems to identify Stackelberg equilibrium points on Hadamard manifolds and under geodesic convexity assumptions

Convex Analysis and Chaos : The Third Symposium on Nonlinear Analysis, July 23-25, 1998 Josai University

We obtain minimax theorerns and the Nash equilibrium theorem forG-convex spaces. Our new results extend and unify a number of known results forparticular types of G-convex spaces. Finally, we compare our new results with thecelebrated minimax theorem of H. K6nig.Convex Analysis and Chaos : The Third Symposium on Nonlinear Analysis, July 23-25, 1998 Josai University, edited by Kiyoko Nishizaw

Geometric Methods of Complex Analysis (hybrid meeting)

The purpose of this workshop was to discuss recent results in Several Complex Variables, Complex Geometry and Complex Dynamical Systems with a special focus on the exchange of ideas and methods among these areas. The main topics of the workshop included Holomorphic Dynamics and Nevanlinna's Theory; $L^2$-methods and Cohomologies; Plurisubharmonic Functions and Pluripotential Theory; Geometric Questions of Complex Analysis

A study of spirallike domains: polynomial convexity, Loewner chains and dense holomorphic curves

In this paper, we prove that the closure of a bounded pseudoconvex domain, which is spirallike with respect to a globally asymptotic stable holomorphic vector field, is polynomially convex. We also provide a necessary and sufficient condition, in terms of polynomial convexity, on a univalent function defined on a strongly convex domain for embedding it into a filtering Loewner chain. Next, we provide an application of our first result. We show that for any bounded pseudoconvex strictly spirallike domain $\Omega$ in $\mathbb{C}^n$ and given any connected complex manifold $Y$, there exists a holomorphic map from the unit disc to the space of all holomorphic maps from $\Omega$ to $Y$. This also yields us the existence of $\mathcal{O}(\Omega, Y)$-universal map for any generalized translation on $\Omega$, which, in turn, is connected to the hypercyclicity of certain composition operators on the space of manifold valued holomorphic maps.Comment: 25 pages, comments are welcom

A Discrete Characterization of the Solvability of Equilibrium Problems and Its Application to Game Theory

We state a characterization of the existence of equilibrium in terms of certain finite subsets under compactness and transfer upper semicontinuity conditions. In order to derive some consequences on game theory—Nash equilibrium and minimax inequalities—we introduce a weak convexity conceptJunta de Andalucia, Project FQM359Maria de Maeztu” Excellence Unit IMAGCEX2020-001105-M, funded by MCIN/AEI/10.13039/501100011033