In this paper we introduce algebraic cone metric spaces, prove some fixed point theorems of contractive mappings on algebraic cone metric spaces, and improve some well-known results in the non-normal case.

Let K be a locally compact hypergroup. In this paper, among other results we give a sufficient condition for the inclusion LΦ1w (K) * LΦ2w (K) ⊆ LΦ1w (K) to hold. Also, as an application, we provide a new sufficient condition for the weighted Orlicz space LΦw (K) to be a convolution Banach algebra.

Purpose This paper aims to introduce a new numerical approach based on the local weak form and the Petrov–Galerkin idea to numerically simulation of a predator–prey system with two-species, two chemicals and an additional chemotactic influence. Design/methodology/approach In the first proceeding, the space derivatives are discretized by using the direct meshless local Petrov–Galerkin method. This generates a nonlinear algebraic system of equations. The mentioned system is solved by using the Broyden’s method which this technique is not related to compute the Jacobian matrix. Findings This current work tries to bring forward a trustworthy and flexible numerical algorithm to simulate the system of predator–prey on the nonrectangular geometries. Originality/value The proposed numerical results confirm that the numerical procedure has acceptable results for the system of partial differential equations.

No abstract