On some new double sequence spaces defined by a modulus

In this paper our purpose is to extend some results known in the literature for ordinary (single) sequences to multiply sequences of real and complex numbers. This will be accomplished by presenting the following sequence spaces: {x∈s″:P-limm,n∑k,l=0,0∞,∞am,n,k,lf(|xσk(p),σl(q)|)pk,l=0}, {x∈s″:P-limm,n∑k,l=0,0∞,∞am,n,k,lf(|xσk(p),σl(q)-Le|)pk,l=0,for someL}, and {x∈s″:supm,n,p,q∑k,l=0,0∞,∞am,n,k,lf(|xσk(p),σl(q)|)pk,l<∞} where f is a modulus function, uniformly in (p, q) and A is a nonnegative RH-regular summability matrix method. In addition, we shall give double σ-statistical convergence.