Rodriguez-Lopez, "Contractive mapping theorems in

partially ordered sets and applications to ordinary differential equations," Order, vol.

Let (Eq.) be a

partially ordered set and (Eq.) According to [BhashkarL], if F is monotone non-decreasing in x and monotone non-increasing in ,y then F is said to have mixed monotone property, that is, for any (Eq.),

[11] Suppose (X, [less than or equal to]) is a

partially ordered set and F, g : X [right arrow] X are mappings of X into itself.

Example 1.1: Let N(P) = {0, 1, I, I [union] 1 = 1 + I, a, aI} be a

partially ordered set; N(P) is a neutrosophic lattice.

Based on the partial-edge order, we can construct a Hasse diagram, which is a directed graph that represents a

partially ordered set (poset).

Therefore, to solve the problem of selecting the staff members, the top k elements among the objects in a

partially ordered set need to be computed, and a hybrid approach that combines the benefits of Skyline and Top-k is required.

The last of the three realizations uses the graph of the

partially ordered set to determine a total ordering.

We also use the notions of a

partially ordered set,

Let [member of] be a

partially ordered set with a partial order '[less than or equal to]' and let (E, p, [less than or equal to]) be a partially ordered hyperbolic metric space.

Key Words:

Partially ordered set, -symmetric property, mixed g -monotone property, Compatible maps, Couple random coincidence point.

Recall that on a

partially ordered set (X, [less than or equal to]) a map T : X [right arrow] X is nondecreasing if it satisfies Tx [less than or equal to] Ty for all x, y [member of] X such that x [less than or equal to] y.

Let (X, [less than or equal to]) be a

partially ordered set. A self mapping T : X [right arrow] X is said to be monotone nondecreasing if Tx [less than or equal to] Ty whenever x [less than or equal to] y, x, y [member of] X.