In this paper, we establish some fixed point results for F⊥-weak contraction in orthogonal metric space and we give an application for the solution of second order differential equation.

The aim of the paper is to obtain some fixed point theorems for extended (ϕ, F)-weak type contraction on a closed ball in metric spaces. Our results generalize some recently established results.

In this paper, the fascinating Julia and Mandelbrot sets for the complex-valued transcendental functions z → sin(z m) + c, (m ≥ 2) ∈ N have been obtained in Picard, Ishikawa and Noor orbits. The purpose of the paper is to visualize transcendental Julia and Mandelbrot sets in Picard-Mann hybrid orbit.