✦ LIBER ✦

Applications of proximal calculus to fixed point theory on Riemannian manifolds

✍ Scribed by Daniel Azagra; Juan Ferrera

Publisher: Elsevier Science
Year: 2007
Tongue: English
Weight: 279 KB
Volume: 67
Category: Article
ISSN: 0362-546X
DOI: 10.1016/j.na.2006.04.019

No coin nor oath required. For personal study only.

✦ Synopsis

We prove a general form of a fixed point theorem for mappings from a Riemannian manifold into itself which are obtained as perturbations of a given mapping by means of general operations which in particular include the cases of sum (when a Lie group structure is given on the manifold) and composition. In order to prove our main result we develop a theory of proximal calculus in the setting of Riemannian manifolds.

📜 SIMILAR VOLUMES

Fixed point theorems and their applicati

Fixed point theorems and their applications to theory of Nash equilibria

✍ S. Heikkilä; K. Reffett 📂 Article 📅 2006 🏛 Elsevier Science 🌐 English ⚖ 235 KB

In this paper we prove fixed point theorems for set-valued mappings in products of posets. Applications to the theory of Nash equilibria are presented.

An application of a fixed-point theorem

An application of a fixed-point theorem to approximation theory

✍ S.P Singh 📂 Article 📅 1979 🏛 Elsevier Science 🌐 English ⚖ 76 KB

Applications of the Proximity Map to Ran

Applications of the Proximity Map to Random Fixed Point Theorems in Hilbert Spaces

✍ I. Beg; N. Shahzad 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 307 KB

Multiple solutions of generalized Yamabe

Multiple solutions of generalized Yamabe equations on Riemannian manifolds and applications to Emden–Fowler problems

✍ Gabriele Bonanno; Giovanni Molica Bisci; Vicenţiu Rădulescu 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 272 KB

A metric on the space of finite measures

A metric on the space of finite measures with an application to fixed point theory

✍ Yonghui Zhou; Jian Yu; Shuwen Xiang 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 225 KB

In this work, we give a metric function on the space of finite measures on a compact metric space, which has some interesting metric properties. As an application, we establish the existence of essential components of the set of fixed points for every upper semicontinuous convex set-valued mapping o

Some generalizations of Ekeland-type var

Some generalizations of Ekeland-type variational principle with applications to equilibrium problems and fixed point theory

✍ S. Al-Homidan; Q.H. Ansari; J.-C. Yao 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 353 KB

In this paper, we introduce the concept of a Q-function defined on a quasi-metric space which generalizes the notion of a τ -function and a w-distance. We establish Ekeland-type variational principles in the setting of quasi-metric spaces with a Q-function. We also present an equilibrium version of