Several Lefschetz fixed point theorems for compact type self maps in new classes of spaces are presented in this paper.

Let (X, d, ) be a partially ordered metric space. Let F, G be two set valued mappings and f , g two single valued mappings on X . We obtained sufficient conditions for existence of common fixed point of F , G, f and g satisfying an implicit relation in X .

In this manuscript, we prove new coupled fixed point theorems extending some recent results in the literature on this topic. We also present applications of these new results through a number of examples.

In this paper, we prove some common fixed point theorems for generalized contractive mappings satisfying some conditions, that is, compatible and compatible-type mappings in multiplicative metric spaces. Our results improve and generalize the corresponding results given in the literature. Moreover, we give some examples to illustrate our main results. c ©2016 All rights reserved.

We show that if a holomorphic n-dimensional compact torus action on a compact connected complex manifold of complex dimension n has a fixed point then the manifold is equivariantly biholomorphic to a smooth toric variety.

In this paper, a new concept of generalized quasi-partial metric spaces is presented. Some fixed point results due to Karapinar et. al., [E. Karapinar, I. M. Erhan, A. Öztürk, Math. Comput. Modelling, 57 (2013), 2442–2448] are extended in the setting of the generalized quasi-partial metric spaces. c ©2016 All rights reserved.

We prove that if F is a finitely generated abelian group of orientation preserving C1 diffeomorphisms of R2 which leaves invariant a compact set then there is a common fixed point for all elements of F . We also show that if F is any abelian subgroup of orientation preserving C1 diffeomorphisms of S2 then there is a common fixed point for all elements of a subgroup of F with index

We give some fixed point theorems for firmly pseudo-contractive mappings defined on nonconvex subsets of a Banach space. We also prove some fixed point results for firmly pseudo-contractive mappings with unbounded nonconvex domain in a reflexive Banach space.

We discuss non existence of analytic first integrals for analytic diffeomorphisms possessing a hyperbolic fixed point with a homoclinic connection.

We characterize the invertible substitutions over a two-letter alphabet which share a common periodic point (or fixed point). The argument is geometrical.