The terms of the sequence are called the parts of the partition.
In such a case, the existence of a coincidence point can be deduced applying the contractivity condition to the terms of the sequence and the desired limit.
As is customary, a solution of (1.11) is said to be oscillatory about zero, or simply oscillatory, if the terms of the sequence are neither eventually all positive nor eventually all negative.
) On these knots, the terms of the sequence of successive approximations are the following: x(t_{i} ) = psi (t_{i} ),quad i = overline{0,n}, x(t_{i} ) = g(t_{i} ) + lambda int_{{t_{i} - tau }}^{{t_{i} }} H(t_{i},s) cdot x s){text{d}}s,quad i = overline{n + 1,q}.
Alternatively, the terms of the sequence after the first can be viewed as the denominators of the odd greedy expansion of 1/2.
where is the forward difference operator and denotes the term of the matrix transform of the sequence, where.
In this paper, we consider the Horadam sequence and some summation formulas involving the terms of the Horadam sequence.
So the iterative method is giving us the terms of the iteration sequence beginning with [0,1].
The last inequality of (5.12) is obtained since, where is just the one in the Step 1. Taking into account the fact that the, we infer that the terms of the numerical sequence are arbitrarily small provided that the number is small enough.
Throughout the paper, we suppose that the terms of the double sequence (x=(x_{mn})) and (y= y_{mn})) are connected with equation (1.3) and the four-dimensional generalized difference matrix (B r,s,t,u)=(b_{mnkl}(r,s,t,u))) will be presented with (B=(b_{mnkl})).
