We study common fixed point theorems for a finite family of discontinuous and noncommutative single-valued functions defined in complete metric spaces. We also study a common fixed point theorem for two multivalued self-mappings and a stationary point theorem in complete metric spaces. Throughout this paper, we establish common fixed point theorems without commuting and continuity assumptions. ...

ABS]RACT. Our main theorem establishes the uniqueness of the common fixed point of tw set-valued mappings and of two single-valued mappings defined on a complete metric space, under a contractive condition and a weak commutativity concept. This improves a theorem of the second author. Let (X,d) be a complete metric space and let B(X) be the set of all nonempty, bounded subsets of X As in [I], l...

Let f be a smooth homeomorphism of the circle having one cubic-exponent critical point and irrational rotation number of bounded combinatorial type. Using certain pull-back and quasi-conformal surgery techniques, we prove that the scaling ratios of f about the critical point are asymptotically independent of f . This settles in particular the golden mean universality conjecture. We introduce th...

On closed orientable 3-manifolds, we consider a class $$ \mathcal{G} of homeomorphisms such that the nonwandering set each f ∈ is finite union surfaces restriction some power fk on these pseudo-Anosov homeomorphism. We prove exist only 3-manifolds form Sg × ℝ/(J(z),r−1), where J : → either homeomorphism surface genus g > 1 or periodic commuting with manifold, construct model and find necessary ...

In 2008, Al-Thaga and Shahzad [Generalized I-nonexpansive self-maps and invariant approximations, Acta Math. Sinica 24(5) (2008), 867{876]introduced the notion of occasionally weakly compatible mappings (shortly owcmaps) which is more general than all the commutativity concepts. In the presentpaper, we prove common xed point theorems for families of owc maps in Mengerspaces. As applications to ...

Introduction. Let/and g be continuous functions mapping the unit interval / into itself which commute under functional composition, that is, f(g(x)) = g(f(x)) for all x in /. In 1954 Eldon Dyer asked whether/and g must always have a common fixed point, meaning a point z in / for which f(z) = z=g(z). A. L. Shields posed the same question independently in 1955, as did Lester Dubins in 1956. The p...