We introduce the notion of relaxed ρ-θ -η-invariant pseudomonotone mappings, which is weaker than invariant pseudomonotone maps. Using the KKM technique, we establish the existence of solutions for variational-like inequality problems with relaxed ρ-θ -η-invariant pseudomonotone mappings in reflexive Banach spaces. We also introduce the concept of ρθ -pseudomonotonicity for bifunctions, and we ...

In this paper we introduce a hybrid relaxed-extragradient method for finding a common element of the set of common fixed points of N nonexpansive mappings and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping. The hybrid relaxed-extragradient method is based on two well-known methods: hybrid and extragradient. We derive a strong convergence ...

Approximation-solvability of a class of nonlinear implicit variational inequalities involving a class of partially relaxed monotone mappings a computation-oriented class in a Hilbert space settingis presented with some applications. Partially Strongly Monotone Mapping, Partially Relaxed Mono

The sub-Riemannian Heisenberg group is the simplest nonabelian example of a Carnot group. Suppose $$(\gamma _k)_{0 \le k m}$$ collection continuous function defined on compact set $$K \subset \mathbb {R}$$ taking values in When there horizontal $$C^{m}$$ curve $$\Gamma $$ so that $$D^k \Gamma |_K = \gamma _k$$ for $$k 0, 1,\dots ,m$$ ? Such extensions are known as “Whitney extensions” due to or...

A new system of generalized mixed quasivariational inclusions for short, SGMQVI with relaxed cocoercive operators, which develop some preexisting variational inequalities, is introduced and investigated in Banach spaces. Next, the existence and uniqueness of solutions to the problem SGMQVI are established in real Banach spaces. From fixed point perspective, we propose some new iterative algorit...

We investigate the convergence properties of a stochastic primal-dual splitting algorithm for solving structured monotone inclusions involving the sum of a cocoercive operator and a composite monotone operator. The proposed method is the stochastic extension to monotone inclusions of a proximal method studied in [26, 35] for saddle point problems. It consists in a forward step determined by the...