Displaying similar documents to “On two open problems of contractive mappings.”

A new class of nonexpansive type mappings and fixed points

Ljubomir B. Ćirić (1999)

Czechoslovak Mathematical Journal

Similarity:

In this paper a new class of self-mappings on metric spaces, which satisfy the nonexpensive type condition (3) below is introduced and investigated. The main result is that such mappings have a unique fixed point. Also, a remetrization theorem, which is converse to Banach contraction principle is given.

Common fixed points of Greguš type multi-valued mappings

R. A. Rashwan, Magdy A. Ahmed (2002)

Archivum Mathematicum

Similarity:

This work is considered as a continuation of [19,20,24]. The concepts of δ -compatibility and sub-compatibility of Li-Shan [19, 20] between a set-valued mapping and a single-valued mapping are used to establish some common fixed point theorems of Greguš type under a φ -type contraction on convex metric spaces. Extensions of known results, especially theorems by Fisher and Sessa [11] (Theorem B below) and Jungck [16] are thereby obtained. An example is given to support our extension. ...

Coincidence and fixed point theorems for nonlinear hybrid generalized contractions

H. K. Pathak, Shin Min Kang, Yeol Je Cho (1998)

Czechoslovak Mathematical Journal

Similarity:

In this paper we first prove some coincidence and fixed point theorems for nonlinear hybrid generalized contractions on metric spaces. Secondly, using the concept of an asymptotically regular sequence, we give some fixed point theorems for Kannan type multi-valued mappings on metric spaces. Our main results improve and extend several known results proved by other authors.