𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Generalized Distance and Existence Theorems in Complete Metric Spaces

✍ Scribed by Tomonari Suzuki

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
143 KB
Volume
253
Category
Article
ISSN
0022-247X

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper, we first introduce the concept of -distance on a metric space, which is a generalized concept of both w-distance and Tataru's distance. We also improve the generalizations of the Banach contraction principle, Caristi's fixed point theorem, Ekeland's variational principle, and the nonconvex minimization theorem according to Takahashi. Further we discuss the relation between w-distance and Tataru's distance.

πŸ“œ SIMILAR VOLUMES

KKM and Ky Fan Theorems in Hyperconvex M
KKM and Ky Fan Theorems in Hyperconvex Metric Spaces
✍ Mohamed A. Khamsi πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 132 KB

In hyperconvex metric spaces, we introduce Knaster᎐Kuratowski᎐Mazurkiewicz mappings. Then we prove an analogue to Ky Fan's fixed point theorem in hyperconvex metric spaces.

Generalized G-KKM Theorems in Generalize
Generalized G-KKM Theorems in Generalized Convex Spaces and Their Applications
✍ Xie Ping Ding πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 129 KB

Some new generalized G-KKM and generalized S-KKM theorems are proved under the noncompact setting of generalized convex spaces. As applications, some new minimax inequalities, saddle point theorems, a coincidence theorem, and a fixed point theorem are given in generalized convex spaces. These theore

A Fixed Point Theorem in Probabilistic M
A Fixed Point Theorem in Probabilistic Metric Spaces and an Application
✍ E. Pap; O. HadΕΎiΔ‡; R. Mesiar πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 198 KB

The notion of a ⌿, C -contraction type multivalued mapping is introduced. This notion is a generalization of the notion of C-contraction introduced by T. L. Hicks Ž .

Existence Theorems of Solutions for Gene
Existence Theorems of Solutions for Generalized Quasi-variational Inequalities, a Minimax Theorem, and a Section Theorem in the Spaces without Linear Structure
✍ Xian Wu πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 176 KB

In this paper, by using particular techniques, two existence theorems of solutions for generalized quasi-variational inequalities, a minimax theorem, and a section theorem in the spaces without linear structure are established; and finally, a new coincidence theorem in locally convex spaces is obtai