In this paper, we find the best proximity point in G-metric spaces for G-generalized ζ-β-T contraction mappings and verify existence uniqueness of complete G metric space using idea an approximatively compact set. addition, example is provided to illustrate outcome.

1.1. Normed spaces. Recall that a (real) vector space V is called a normed space if there exists a function ‖ · ‖ : V → R such that (1) ‖f‖ ≥ 0 for all f ∈ V and ‖f‖ = 0 if and only if f = 0. (2) ‖af‖ = |a| ‖f‖ for all f ∈ V and all scalars a. (3) (Triangle inequality) ‖f + g‖ ≤ ‖f ||+ ‖g‖ for all f, g ∈ V . If V is a normed space, then d(f, g) = ‖f−g‖ defines a metric on V . Convergence w.r.t ...

‎The purpose of this paper is to establish some coupled coincidence point theorems for mappings having a mixed $g$-monotone property in partially ordered metric spaces‎. ‎Also‎, ‎we present a result on the existence and uniqueness of coupled common fixed points‎. ‎The results presented in the paper generalize and extend several well-known results in the literature‎.

1 1 INTRODUCTION 2 1 Introduction Classical calculus is a basic tool in analysis. We use it so often that we forget that its construction needed considerable time and effort. Especially in the last decade, the progresses made in the field of analysis in metric spaces make us reconsider this calculus. Along this line of thought, all started with the definition of Pansu derivative [24] and its ve...

Geodesic orbit spaces (or g.o. spaces) are defined as those homogeneous Riemannian (M=G∕H,g) whose geodesics orbits of one-parameter subgroups G. The corresponding metric g is called a geodesic metric. We study the form (Sp(n)∕Sp(n1)×⋯×Sp(ns),g), with 0<n1+⋯+ns≤n. Such include spheres, quaternionic Stiefel manifolds, Grassmann manifolds and flag manifolds. present work contribution to (G∕H,g) H...

We prove that, starting at an initial metric g(0) = e2u0(dx2 + dy2) on R2 with bounded scalar curvature and bounded u0, the Ricci flow ∂tg(t) = −Rg(t)g(t) converges to a flat metric on R2.

In this paper, we prove that Kähler-Ricci flow converges to a Kähler-Einstein metric (or a Kähler-Ricci soliton) in the sense of Cheeger-Gromov as long as an initial Kähler metric is very closed to gKE (or gKS) if a compact Kähler manifold with c1(M) > 0 admits a Kähler Einstein metric gKE (or a Kähler-Ricci soliton gKS). The result improves Main Theorem in [TZ3] in the sense of stability of Kä...

For an ordered set W = {w1, w2, . . . , wk} of vertices and a vertex v in a connected graph G, the ordered k-vector r(v|W ) := (d(v, w1), d(v, w2), . . . , d(v, wk)) is called the metric representation of v with respect to W , where d(x, y) is the distance between vertices x and y. A set W is called a resolving set for G if distinct vertices of G have distinct representations with respect to W ...

In this paper we introduced the (E.A.)-property and weak compatibility of mappings in G-metric spaces. We have utilized these concepts to deduce certain common fixed point theorems in G-metric space

For a compact Riemannian manifold (M, g) with boundary and dimension n, with n ≥ 2, we study the existence of metrics in the conformal class of g with scalar curvature Rg and mean curvature hg on the boundary. In this paper we find sufficient and necessary conditions for the existence of a smaller metric g̃ < g with curvatures Rg̃ = Rg and hg̃ = hg. Furthermore, we establish the uniqueness of such...