The purpose of this paper is to find of the theoretical results of fixed point theorems for a mixed monotone mapping in a metric space endowed with partially order by using the generalized Kanann type contractivity of assumption. Also, as an application, we prove the existence and uniqueness of solution for a first-order ordinary differential equation with periodic bou...

The problem of monotonicity testing of the boolean hypercube is a classic well-studied, yet unsolved question in property testing. We are given query access to f : {0, 1} 7→ R (for some ordered range R). The boolean hypercube B has a natural partial order, denoted by ≺ (defined by the product of coordinate-wise ordering). A function is monotone if all pairs x ≺ y in B, f(x) ≤ f(y). The distance...

1 Overview 1.1 Last time • Proper learning for P implies property testing of P (generic, but quite inefficient) • Testing linearity (over GF[2]), i.e. P = {all parities}: (optimal) O 1-query 1-sided non-adaptive tester. • Testing monotonicity (P = {all monotone functions}: an efficient O n-query 1-sided non-adaptive tester.

In this paper, we introduce a new class of monotone operators − (H(·, ·), η)monotone operators, which generalize many existing monotone operators. The resolvent operator associated with an (H(·, ·), η)monotone operator is defined and its Lipschitz continuity is presented. As an application, we also consider a new generalized mixed variational inclusion involving (H(·, ·), η)-monotone operators ...

Given a monotone property P of graphs, write Pn for the set of graphs with vertex set [n] having property P. Building on recent results in the enumeration of graphical properties, we prove numerous results about the structure of graphs in Pn and the functions |Pn|. We also examine the measure eP (n), the maximum number of edges in a graph of Pn.

Absac A graph property is called elusive (or evasive) if every algorithm for testing this property has to read in the worst case Q) entries of the adjacency matrix of the given graph. Several graph properties have been shown to be elusive, e.g. planarity [2] or fc-colorability [4]. A famous conjecture of Karp [11] says that every non-trivial monotone graph property is elusive. We prove that a n...