Human color vision starts with the signals from three cone photoreceptor types, maximally sensitive to long (L-cone), middle (M-cone), and short (S-cone) wavelengths. Within the retina these signals combine in an antagonistic way to form red-green and blue-yellow spectral opponent pathways. In the classical model this antagonism is thought to arise from the convergence of cone type-specific exc...

Densitometry is a powerful tool for the biophysical assessment of the retina. Until recently, this was restricted to bulk spatial scales in living humans. The application of adaptive optics (AO) to the conventional fundus camera and scanning laser ophthalmoscope (SLO) has begun to translate these studies to cellular scales. Here, we employ an AOSLO to perform dynamic photopigment densitometry i...

Consider two finite-dimensional normed spaces X and Y , a fixed convex cone K ⊂ X, and a linear mapping A : X → Y . We call A well-posed if AK = Y . In particular, in the purely linear case K = X, well-posedness coincides with surjectivity. Our interest is in the “distance to ill-posedness”: that is, we seek the smallest structured linear perturbation ∆A : X → Y such that the perturbed mapping ...

In this paper, we consider a bilevel vector optimization problem where objective and constraints are set valued maps. Our approach consists of using a support function [1, 2, 3, 14, 15, 32] together with the convex separation principle for the study of necessary optimality conditions for D.C bilevel set valued optimization problems. We give optimality conditions in terms of the strong subdiffer...

In the solution methods of the symmetric cone complementarity problem (SCCP), the squared norm of a complementarity function serves naturally as a merit function for the problem itself or the equivalent system of equations reformulation. In this paper, we study the growth behavior of two classes of such merit functions, which are induced by the smooth EP complementarity functions and the smooth...

It is well known that the classical contraction mapping principle of Banach is a fundamental result in fixed point theory. Several authors have obtained various extensions and generalizations of Banach’s theorems by considering contractive mappings on different metric spaces. Huang and Zhang [1] have replaced real numbers by ordering Banach space and have defined a cone metric space. They have ...

Recently, José R. Morales and Edixon Rojas [José R. Morales and Edixon Rojas, Cone metric spaces and fixed point theorems of T -Kannan contractive mappings, Int. J. Math. Anal. 4 (4) (2010) 175–184] proved fixed point theorems for T -Kannan and T -Chatterjea contractions in conemetric spaces when the underlying cone is normal. The aim of this paper is to prove this without using the normality c...

We discuss the newly introduced concept of cone metric spaces. We also discuss the fixed point existence results of contractive mappings defined on such metric spaces. In particular, we show that most of the new results are merely copies of the classical ones.

The aim of this paper is to establish some common random fixed point theorems under contractive type condition in the framework of cone random metric spaces and also to obtain some classical results as corollaries. Our results extend and generalize many known results from the current existing literature.