Using the piecewise monotone property, we give a full description of non-monotonicity height of PM functions with a single fort on compact interval. This method is also available for general PM functions with finitely many forts, as well as those functions defined on the whole real line. Finally, we obtain a sufficient and necessary condition for the finite non-monotonicity height by characteri...

We survey a number of minor-monotone graph parameters and their relationship to the complexity of routing on graphs. In particular we compare the interval routing parameters κslir(G) and κsir(G) with Colin de Verdière’s graph invariant μ(G) and its variants λ(G) and κ(G). We show that for all the known characterizations of θ(G) with θ(G) being μ(G), λ(G) or κ(G), that θ(G) ≤ 2κslir(G) − 1 and θ...

* Correspondence: [email protected] Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia Abstract Using the notion of compatible mappings in the setting of a partially ordered metric space, we prove the existence and uniqueness of coupled coincidence points involving a (j, ψ)-contractive condition for a mappings having the mixed g-monotone propert...

In this paper, we consider several property testing problems and ask how the query complexity depends on the distance parameter ǫ. We achieve new lower bounds in this setting for the problems of testing whether a function is monotone and testing whether the function has low Fourier degree. For monotonicity testing, our lower bound matches the recent upper bound of Chakrabarty and Seshadhri [12].

A Boolean k-monotone function defined over a finite poset domain D alternates between the values 0 and 1 at most k times on any ascending chain in D. Therefore, k-monotone functions are natural generalizations of the classical monotone functions, which are the 1-monotone functions. Motivated by the recent interest in k-monotone functions in the context of circuit complexity and learning theory,...

we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}, $h$-...

In this work we are concerned with maximality of monotone operators representable by certain convex functions in non-reflexive Banach spaces. We also prove that these maximal monotone operators satisfy a Brønsted-Rockafellar type property. 2000 Mathematics Subject Classification: 47H05, 49J52, 47N10.

In this paper, we prove existence of a coupled coincidence point theorem and coupled common fixed point theorem for φ-contractive mappings in partially ordered complete metric space without the mixed g-monotone property by using the concept of an (F, g)-invariant set. We prove some coupled fixed point theorems for such nonlinear contractive mappings in a complete metric space.Our results are ge...