Existence Results for Generalized Vector Quasi-Equilibrium Problems in Hadamard Manifolds

The purpose of this article was to establish manifold versions of existence theorems for generalized vector quasi-equilibrium problems in locally compact and σ-compact spaces without any continuity assumption. The fixed-point theorem in a product Hadamard manifold is the key focus of our discussion. We further applied our theorems to saddle point and minimax problems

GENERALIZED HECKE GROUPS AND HECKE POLYGONS

Abstract. In this paper, we study certain Fuchsian groups H (p1,...,pn), called generalized Hecke groups. These groups are isomorphic to ∏ ∗ n j=1Zpj. Let Γ be a subgroup of finite index in H (p1,...,pn). By Kurosh’s theorem, Γ is isomorphic to Fr ∗ ∏ ∗ k i=1Zmi,whereFris a free group of rank r,andeachmidivides some pj. Moreover, H2 /Γ is Riemann surface. The numbers m1,...,mk are branching numbers of the branch points on H2 /Γ. The signatureofΓ is (g; m1,...,mk; t), whereg and t are the genus and the number of cusps of H2 /Γ, respectively. A purpose of this paper is to consider two problems. First, determine the necessary and sufficient conditions for the existence of a subgroup of finite index of a given type in H (p1,...,pn). We also extend this work to extended generalized Hecke groups H ∗ (p1,...,pn) whichareisomorphic to Dp1 ∗Z

Existence theorems for generalized vector variational inequalities with a variable ordering relation

Generalized vector variational inequality, Variable ordering relation, Cone mapping, KKM-Fan theorem, Brouwer fixed point theorem, Monotonicity, Complete continuity, Primary 49J30, 47H10, 47H17,