In this paper, some new existence and convergence theorems of best proximity point for new nonlinear cyclic maps are established. These results generalize and improve some main results in [5, 20, 21] and references therein.

In this paper, two important issues about the discrete version of Caputo’s fractional-order maps defined on complex plane are investigated, both analytically and numerically: attractors symmetry-breaking induced by derivative sensitivity in determining bifurcation diagram. It is proved that integer-order with dihedral symmetry or cycle may lose their once they transformed to maps. Also, it conj...

A Cayley map is a 2-cell embedding of a Cayley graph into an orientable surface with the same local orientation induced by a cyclic permutation of generators at each vertex. In this paper, we provide classifications of prime-valent regular Cayley maps on abelian groups, dihedral groups and dicyclic groups. Consequently, we show that all prime-valent regular Cayley maps on dihedral groups are ba...

For spacetimes containing quiescent singularity hypersurfaces we propose a general notion of junction conditions based on prescribed scattering map, as call it, and introduce the cyclic spacetime (also called multiverse) consisting domains bounded by spacelike or timelike hypersurfaces, across which our map is applied. A local existence theory established here while, in companion paper, constru...