In this paper, we investigate relation between weak subdifferential and augmented normal cone. We define augmented normal cone via weak subdifferential and vice versa. The necessary conditions for the global maximum are also stated. We produce preliminary properties of augmented normal cones and discuss them via the distance function. Then we obtain the augmented normal cone for the indicator f...

Zero-index materials exhibit exotic optical properties that can be utilized for integrated-optics applications. However, practical implementation requires compatibility with complementary metallic-oxide-semiconductor (CMOS) technologies. We demonstrate a CMOS-compatible zero-index metamaterial consisting of a square array of air holes in a 220-nm-thick silicon-on-insulator (SOI) wafer. This des...

‎The aim of this paper is to establish the equivalence between the concepts‎ ‎of an $S$-metric space and a cone $S$-metric space using some topological‎ ‎approaches‎. ‎We introduce a new notion of a $TVS$-cone $S$-metric space using‎ ‎some facts about topological vector spaces‎. ‎We see that the known results on‎ ‎cone $S$-metric spaces (or $N$-cone metric spaces) can be directly obtained‎ from...

Our theorems are on ordered cone metric spaces which are not necessarily normal. In the end, we describe the application of the main results in the integral equation.Although Du in [W‎. ‎S‎. ‎Du‎, ‎A note on cone metric fixed point theory and its equivalence‎, ‎Nonlinear Analysis‎, ‎72(2010) 2259-2261.]‎, ‎showed that the fixed point results in the setting of cone...

In optical tomography, there exist certain spatial frequency components that cannot be measured due to the limited projection angles imposed by the numerical aperture of objective lenses. This limitation, often called as the missing cone problem, causes the under-estimation of refractive index (RI) values in tomograms and results in severe elongations of RI distributions along the optical axis....

In this paper some existence and nonexistence results for positive solutions are obtained for second-order boundary value problem −u + Mu = f(t, u), t ∈ (0, 1) with Neumann boundary conditions u(0) = u(1) = 0, where M > 0, f ∈ C([0, 1] × R, R). By making use of fixed point index theory in cones, some new results are obtained. Full text

Let (X, d) be a complete partially ordered cone metric space, g : X → X and F : X × X × X → X be two mappings. In this paper, a new concept of F having the mixed comparable property with respect to g is introduced and some tripled coincidence point results of F and g are obtained if F has the mixed comparable property with respect to g and some other natural conditions are satisfied. Moreover, ...