We prove some coupled fixed point theorems for mappings satisfying different contractive conditions on complete cone metric spaces.

Electrochemical noise (EN) and electrochemical impedance spectroscopy (EIS) measurements were used to evaluate protective properties and corrosion behaviour of two different organic coating systems. The coatings of commercial grade (zinc rich ethyl silicate) were applied to steel substrates and immersed for up to 3 months in 0 . 5M NaCl at 25uC. An analysis of the EN data was performed during this time, including the measurements of the mean potential E mean , the mean current I mean and the noise resistance R n . The time series noise patterns were transformed into frequency domain by fast Fourier transformation. The power spectral densities (PSDs) of the potential and of the current and roll off slope coatings were then compared with each other. These coated plates were assessed by EIS. Electrolytic penetration through the coating, changes in the dynamic characteristics of the conduction and resistance of the coating film of the protected system as a function of time. Equivalent circuits were used to interpret the physical and electrochemical properties. The mechanism and kinetics of the electrochemical systems were assessed by measuring the fluctuations in capacitance and percentage of water uptake. The coatings were evaluated in salt spray and humidity tests according to ASTM B117 and D2247.

Matthews [12] introduced a new distance P on a nonempty set X, which he called a partial metric. The purpose of this paper is to present some fixed point results for weakly contractive type mappings in ordered partial metric space. An application to nonlinear fractional boundary value problem is also presented.

In this paper, we consider a multiterm semilinear fractional boundary value problem involving Caputo fractional derivatives and investigate the existence of positive solutions by terms of different given conditions. To do this, we first study the properties of Green’s function, and then by defining two lower and upper control functions and using the wellknown Schauder’s fixed-point theorem, we obtain the desired existence criteria. At the end of the paper, we provide a numerical example based on the given boundary value problem and obtain its upper and lower solutions, and finally, we compare these positive solutions with exact solution graphically.

We define the concept of generalized ϕ-pair mappings and prove some common fixed point theorems for this type of mappings. Our results generalize some recent results.