(i) ; (ii)for which satisfies, ; (iii)for, and,.
By hypothesis there exists a for which satisfies a constraint qualification [14, pages 102-103] for (1.8).
Throughout the paper we suggest to impose one of the following conditions: (a) the Banach space is 2-uniformly smooth; (b) there exists a constant for which satisfies the following inequality: (3).
Denote by the class of analytic functions given by which satisfy for all.
It's not only dangerous when it produces the communists, the Jacobins and the Nazis, but also in the context of democratic or liberal meliorism, because it creates a preference for policies which satisfy this need for meaning rather than have an actual effect".
Throughout this paper, we need the following hypotheses: (H1) are continuous and for ; (H2) with ; (H3) is nondecreasing, is nonincreasing, and there exist on interval with, for all, there exists such that, and for all which satisfy (1.7).
Suppose that is a sequence in generated iteratively by,, for all, where,, and are three real sequences in for some which satisfy condition.
If we suppose that (1.1) is nonoscillatory, among all solutions of (2.1) there exists the so-calleddistinguished solution which has the property that there exists an interval such that any other solution of (2.1) for which,, satisfies,.
In 2006, Bhaskar and Lakshmikantham [20] introduced the concept of a mixed monotone property for the first time and gave their classical coupled fixed point theorems for mappings which satisfy the mixed monotone property.
