Abstract. In this paper, we aim to prove certain common fixed point theorems for a pair of weakly compatible mappings satisfying (CLRg) (or (E.A)) property in the bicomplex valued metric spaces. We also provide some examples which support the main results here.

The relative order of growth gives a quantitative assessment of how different functions scale each other and to what extent they are self-similar in growth. In this paper for any two positive integerspandq, we wish to introduce an alternative definition of relative(p,q)th order which improves the earlier definition of relative(p,q)th order as introduced by Lahiri and Banerjee (2005). Also in this paper we discuss some growth rates of entire functions on the basis of the improved definition of relative(p,q)th order with respect to another entire function and extend some earlier concepts as given by Lahiri and Banerjee (2005), providing some examples of entire functions whose growth rate can accordingly be studied.

In the paper we establish some new results depending on the comparative growth properties of composite entire or meromorphic functions using generalised L∗-order and generalised L∗-type and Wronskians generated by one of the factors.

In the paper we prove some comparative growth properties of composite entire functions on the basis of their maximum terms and maximum moduli using generalised L * -order and generalised L * -lower order.

Abstract:In this paper we introduce the idea of relative Ritt L * -type and relative RittL * -weak type of entire functions represented by vector valued dirichlet series. Further we wish to study some growth properties of entire functions represented by a vector valued Dirichlet series on the basis of relative Ritt L * -type and relative Ritt L * -weak type.