On a fixed point theorem of Krasnosel'skii type and application to integral equations.
In questa nota mostriamo come un teorema di esistenza per funzionali lineari porti un nuovo teorema di punto fisso che generalizza un teorema di punto fisso di Cellina.
Let be a closed convex subset of a complete convex metric space . In this paper a class of selfmappings on , which satisfy the nonexpansive type condition below, is introduced and investigated. The main result is that such mappings have a unique fixed point.
Let be a uniformly convex Banach space, , a nonexpansive map, and a closed bounded subset such that . If (1) is weakly inward and is star-shaped or (2) satisfies the Leray-Schauder boundary condition, then has a fixed point in . This is closely related to a problem of Gulevich [Gu]. Some of our main results are generalizations of theorems due to Kirk and Ray [KR] and others.
In this contribution, we discuss some unique common fixed point theorems for three and four occasionally weakly compatible mappings satisfying different types of contractive condition.