In this paper, we generalize and prove common fixed point theorems of generalized contractive maps in complete cone metric spaces. Our theorems improve and generalize of the results [7].

In common fixed point results for two maps defined on a G−cone metric space, satisfying generalized contractive conditions are obtained. These results generalize, improve and unify several well known comparable results in the literature.

Given a closed convex cone C in a finite dimensional real Hilbert space H, a weakly homogeneous map f : C → H is a sum of two continuous maps h and g, where h is positively homogeneous of degree γ (≥ 0) on C and g(x) = o(||x||) as ||x|| → ∞ in C. Given such a map f , a nonempty closed convex subset K of C, and a q ∈ H, we consider the variational inequality problem, VI(f,K, q), of finding an x∗...

in this paper, using clarke’s generalized directional derivative and di-invexity we introduce new concepts of nonsmooth k-α-di-invex and generalized type i univex functions over cones for a nonsmooth vector optimization problem with cone constraints. we obtain some sufficient optimality conditions and mond-weir type duality results under the foresaid generalized invexity and type i cone-univexi...

It is known that vector variational inequality models arises from vector optimization and vector traac equilibria. In this paper, existence results of a solution for a generalized pre-vector variational inequality and a generalized pre-quasi-vector variational inequality are established. The main condition used is that the underlying vector-valued function is assumed to be cone-quasi-convex. Th...

In this paper we study sensitivity analysis of generalized equations (variational inequalities) with nonpolyhedral set constraints. We use an approach of local reduction of the corresponding constraint set to a convex cone. This leads to an introduction of an additional term in a linearization of the generalized equations which represents a curvature of the constraint set. We also discuss conce...

Here, we extend the notion of (E.A.) property in a convex metric space defined by Kumar and Rathee (Fixed Point Theory Appl 1-14, 2014) by introducing a new class of self-maps which satisfies the common property (E.A.) in the context of convex metric space and ensure the existence of common fixed point for this newly introduced class of self-maps. Also, we guarantee the existence of common best...

We give a formula for the Lipschitz constant in Thompson’s part metric of any order-preserving flow on the interior of a (possibly infinite dimensional) closed convex pointed cone. This provides an explicit form of a characterization of Nussbaum concerning non order-preserving flows. As an application of this formula, we show that the flow of the generalized Riccati equation arising in stochast...