The generalized parallel sum of two monotone operators via a linear continuous mapping is defined as the inverse of the sum of the inverse of one of the operators and with inverse of the composition of the second one with the linear continuous mapping. In this article, by assuming that the operators are maximal monotone of Gossez type (D), we provide sufficient conditions of both interiorityand...

In this paper, we present some new results on the existence of solutions generalized variational inequalities for set-valued mappings in reflexive Banach spaces with Fréchet differentiable norms. Moreover, structure solution sets is investigated. The result obtained paper improves and extends ones announced by Fang Peterson [S. C. E. L. Peterson, Generalized Variational Inequalities, J. Optim. ...

We examine the linear convergence rates of variants of the proximal point method for finding zeros of maximal monotone operators. We begin by showing how metric subregularity is sufficient for linear convergence to a zero of a maximal monotone operator. This result is then generalized to obtain convergence rates for the problem of finding a common zero of multiple monotone operators by consider...

Extending the concept of level measure μ({f⩾a}) we introduce a generalized based on family conditional aggregations operators. As recent research direction, aggregation operators extend in order to model dependence function set. Generalized measures then provide new insight into behaviour level-dependent (monotone) and related processes. We investigate detail several basic properties measure, i...

‎In this paper‎, ‎some properties of pre-monotone operators are proved‎. ‎It is shown that in a reflexive Banach space‎, ‎a full domain multivalued $sigma$-monotone operator with sequentially norm$times$weak$^*$ closed graph is norm$times$weak$^*$ upper semicontinuous‎. ‎The notion of $sigma$-convexity is introduced and the‎ ‎relations between the $sigma$-monotonicity and $sigma$-convexity is i...

We introduce and study a class of a system of random set-valued variational inclusion problems. Some conditions for the existence of solutions of such problems are provided, when the operators are contained in the classes of generalized monotone operators, so-called A,m, η -monotone operator. Further, the stability of the iterative algorithm for finding a solution of the considered problem is a...

In this paper we establish the existence and uniqueness of solutions for nonlinear evolution equations on Banach space with locally monotone operators, which is a generalization of the classical result by J.L. Lions for monotone operators. In particular, we show that local monotonicity implies the pseudo-monotonicity. The main result is applied to various types of PDE such as reaction-diffusion...