Sentence examples for with respect to a cone from inspiring English sources

We define a new concept of integral with respect to a cone.

In this paper, we establish new Poisson type inequalities with respect to a cone.

Section 3 contains the main existence theorems for positive solutions with respect to a cone for our problem (S - BC).

In this paper, we discussed the improved Poisson type inequalities with respect to a cone only using gradient information.

Also, in 2011 Khojasteh and Razani [11] introduced the concept of integral with respect to a cone.

In Section 3, we prove some nonexistence results for the positive solutions with respect to a cone for our problem (S - BC).

Many authors [2 7] have established a generalized version of these two results in different settings, that is, in vector-valued generalized metric space with respect to a convex cone (mathbb{K}) in a Banach space.

As special cases we get the corresponding fixed point theorems on a cone metric space with respect to a solid cone.

As special cases we get the corresponding fixed point theorems in a cone metric space with respect to a solid cone.

In this paper, we establish new fixed point results for multi-valued operator on a cone metric space with respect to a solid cone by using the idea of the generalized Hausdorff distance due to Cho and Bae (Fixed Point Theory Appl. 2011 87, 2011).

Let (X, ||·|| c ) be a cone normed space with respect to a normal cone P in the real Banach space E, and { T n } n ∈ N 0 be a sequence of self-maps of X with ∩ n F(T n ) ≠ ∅, T0 = I and d c (T n x, q) ≤ (1 + α n ) d c (x, q) for all n ∈ N 0, x ∈ X and q ��� ∩ n F(T n ) where ∑ n ∈ N 0 α n < ∞.