Running Homoclinic and Periodic Points in Standard-Like Mappings

Homoclinic Points

Fixed Point Indices and Periodic Points of Holomorphic Mappings

Let ∆ be the ball |x| < 1 in the complex vector space C, let f : ∆ → C be a holomorphic mapping and let M be a positive integer. Assume that the origin 0 = (0, . . . , 0) is an isolated fixed point of both f and the M -th iteration f of f . Then for each factor m of M, the origin is again an isolated fixed point of f and the fixed point index μfm(0) of f m at the origin is well defined, and so ...

Fixed Points, Periodic Points, and Coin-tossing Sequences for Mappings Defined on Two-dimensional Cells

We propose, in the general setting of topological spaces, a definition of two-dimensional oriented cell and consider maps which possess a property of stretching along the paths with respect to oriented cells. For these maps, we prove some theorems on the existence of fixed points, periodic points, and sequences of iterates which are chaotic in a suitable manner. Our results, motivated by the st...

Fixed Points of Contractive Mappings in b-Metric-Like Spaces

We discuss topological structure of b-metric-like spaces and demonstrate a fundamental lemma for the convergence of sequences. As an application we prove certain fixed point results in the setup of such spaces for different types of contractive mappings. Finally, some periodic point results in b-metric-like spaces are obtained. Two examples are presented in order to verify the effectiveness and...

Coincidence Points and Common Fixed Points for Expansive Type Mappings in $b$-Metric Spaces

The main purpose of this paper is to obtain sufficient conditions for existence of points of coincidence and common fixed points for a pair of self mappings satisfying some expansive type conditions in $b$-metric spaces. Finally, we investigate that the equivalence of one of these results in the context of cone $b$-metric spaces cannot be obtained by the techniques using scalarization function....