And also suppose that X has the (OC) property.
Suppose that the assumptions of Theorem 2.1 hold, and also suppose (2.5).
Now suppose that, and also suppose that there are at most local extrema points.
for all for which and Suppose that and is continuous and commutes with, and also suppose that either.
Suppose F(X × X) ⊆ g(X), g is continuous and compatible with F and also suppose either.
Suppose that ( X, τ ) is a topological space, and also suppose that ( Y, N ) is a minimal space.
Assume there is a function with and for each, and also suppose that and such that has the mixed -monotone property and (13).
Suppose T ( X k ) ⊂ G ( X k ) and also suppose either (a) T is continuous, G is continuous and commutes with T or (b) ( X, d, ≤ ) is regular and G ( X k ) is closed. .
For that reason, citizens are supposed to collect and treat all their wastewater and also supposed to pay a water cess proportional to their water consumption to the local State Pollution Control Board (SPCB).
Suppose F ( X 2 ) ⊂ g ( X ) and also suppose either (a) F is continuous, g is continuous and commutes with F or (b) ( X, d, ≤ ) is regular and g ( X ) is closed. .
Suppose that F ( X × X ) ⊆ g ( X ), g is continuous and commutes with F, and also suppose that either (a) F is continuous, or (b) X has the following property: (i) If a non-decreasing sequence { x n } → x, then x n ≤ x for all n; (ii) If a non-increasing sequence { y n } → y, then y ≤ y n for all n. .
