Fixed Point Theorems for Hybrid Mappings

We obtain some fixed point theorems for two pairs of hybrid mappings using hybrid tangential property and quadratic type contractive condition. Our results generalize some results by Babu and Alemayehu and those contained therein. In the sequel, we introduce a new notion to generalize occasionally weak compatibility. Moreover, two concrete examples are established to illuminate the generality of our results.

VIII. (I.) On a tangential property of regular hypoeycloids and epicycloids. (II.) On theorems relating to the regular polyhedra which are analogous to those of Dr. Matthew Stewart on the regular polygons

1. The following theorems will be established :— (A.) The product of the perpendiculars drawn from all the cusps in each of these roulettes on any tangent is a function of the perpen­dicular only, which is drawn on the same tangent from the centre of the fixed circle, on which the roulette is generated.