Fixed points of cone compression and expansion multimaps defined on Fréchet spaces: The projective limit approach

Fixed Points of Cone Compression and Expansion Multimaps Defined on Frechet Spaces: the Projective Limit Approach

This paper presents cone compression and expansion fixed point results of KrasnoselskiiPetryshyn type formultimaps between Fréchet spaces. Two approaches have recently been presented in the literature, both of which are based on the fact that a Fréchet space can be viewed as a projective limit of a sequence of Banach spaces {En}n∈N (here N= {1,2, . . .}). Both approaches are based on constructi...

Fixed point theory for Mönch-type maps defined on closed subsets of Fréchet spaces: the projective limit approach

This paper presents new Leray-Schauder alternatives for Mönch-type maps defined between Fréchet spaces. Two approaches [1, 2, 3, 6, 7] have recently been presented in the literature both of which are based on the fact that a Fréchet space can be viewed as a projective limit of a sequence of Banach spaces {En}n∈N (here N = {1,2, . . .}). Both approaches are based on constructing maps Fn defined ...

Fixed Points for w-Contractive Multimaps

Fixed Points for Contractive Type Multimaps

Without using the concept of the Hausdorff metric, we prove some results on the existence of fixed points and strict fixed points for multivalued maps satisfying some generalized Latif-Albar type conditions. Consequently, several known fixed point results either generalized or improved including the corresponding recent results of Feng and Liu [J. Math. Anal. Appl. 317 (2006) 103-112], Latif an...

FIXED POINTS OF n-VALUED MULTIMAPS OF THE CIRCLE

A multifunction φ : X ( Y is n-valued if φ(x) is an unordered subset of n points of Y for each x ∈ X. The (continuous) n-valued multimaps φ : S ( S are classified up to homotopy by an integer-valued degree. In the Nielsen fixed point theory of such multimaps, due to Schirmer, the Nielsen number N(φ) of an n-valued φ : S ( S of degree d equals |n − d| and φ is homotopic to an n-valued power map ...