In the present paper, we introduces the notion of integral type contractive mapping with respect to ordered S-metric space and prove some coupled common fixed point results of integral type contractive mapping in ordered S-metric space. Moreover, we give an example to support our main result.

The aim of this paper is to prove coupled coincidence and coupled common fixed point theorems for a mixed g-monotone mapping satisfying nonlinear contractive conditions in the setting of partially ordered G-metric spaces. Present theorems are true generalizations of the recent results of Choudhury and Maity [Math Comput. Modelling 54 (2011), 73–79], and Luong and Thuan [Math. Comput. Modelling ...

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...

In this paper, we initiate a systematic study of graph resilience. The (local) resilience of a graph G with respect to a property P measures how much one has to change G (locally) in order to destroy P . Estimating the resilience leads to many new and challenging problems. Here we focus on random and pseudo-random graphs and prove several sharp results. 1 The notion of resilience A typical resu...

In their seminal work which initiated random graph theory Erd os and R enyi discovered that many graph properties have sharp thresholds as the number of vertices tends to in nity We prove a conjecture of Linial that every monotone graph property has a sharp threshold This follows from the following theorem Let Vn p f g denote the Hamming space endowed with the probability measure p de ned by p ...

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.