We prove uniform convexity of solutions to the capillarity boundary value problem for fixed boundary angle in (0, π/2) and strictly positive capillarity constant provided that the base domain Ω ⊂ R is sufficiently close to a disk in a suitable C-sense.

In this paper, we prove strong convergence results for a modified Mann iterative process for a new class of I- nearly weak uniformly L-Lipschitzian mappings in a real Banach space. The class of I-nearly weak uniformly L-Lipschitzian mappings is an interesting generalization of the class of nearly weak uniformly L-Lipschitzian mappings which inturn is a generalization of the class of nearly unif...

M. Gromov [8] suggested to use uniform embeddings into a Hilbert space or into a uniformly convex space as a tool for solving some of the well-known problems. G. Yu [20] and G. Kasparov and G. Yu [10] have shown that this is indeed a very powerful tool. G. Yu in [20] used the condition of embeddability into a Hilbert space; G. Kasparov and G. Yu [10] used the condition of embeddability into a g...

In this paper we introduce new modified implicit and explicit algorithms and prove strong convergence of the two algorithms to a common fixed point of a family of uniformly asymptotically regular asymptotically nonexpansive mappings in a real reflexive Banach space  with a uniformly G$hat{a}$teaux differentiable norm. Our result is applicable in $L_{p}(ell_{p})$ spaces, $1 < p

We prove that Hilbert geometries on uniformly convex Euclidean domains with C 2-boundaries are roughly isometric to the real hyperbolic spaces of corresponding dimension.

The purpose of this note is to present two elementary, but useful, facts concerning actions on uniformly convex spaces. We demonstrate how each of them can be used in an alternative proof of the triviality of the first Lp-cohomology of higher rank simple Lie groups, proved in [1]. Let G be a locally compact group with a compact generating set K ∋ 1, and let X be a complete Busemann non-positive...

Let Cb(K) be the set of all bounded continuous (real or complex) functions on a complete metric space K and A a closed subspace of Cb(K). Using the variational method, it is shown that the set of all strong peak functions in A is dense if and only if the set of all strong peak points is a norming subset of A. As a corollary we show that if X is a locally uniformly convex, complex Banach space, ...

Let $E$ be a uniformly smooth and convex real Banach space $E^*$ its dual space. Suppose $A : E\rightarrow E^*$ is bounded, strongly monotone satisfies the range condition such that $A^{-1}(0)\neq \emptyset$. Inspired by Alber [2], we introduce Lyapunov functions use new geometric properties of spaces to show strong convergence an iterative algorithm solution $Ax=0$.

We introduce a Halpern-type iteration for a generalized mixed equilibrium problem in uniformly smooth and uniformly convex Banach spaces. Strong convergence theorems are also established in this paper. As applications, we apply our main result to mixed equilibrium, generalized equilibrium, and mixed variational inequality problems in Banach spaces. Finally, examples and numerical results are al...