Following the ideas of stronger forms of monotonicity for unary real functions and for capacities, k-monotone and strongly kmonotone aggregation functions are introduced and discussed. In the special case k = 2 also some applications are given.

In this paper, we propose and study several strongly convergent versions of the forward–reflected–backward splitting method Malitsky Tam for finding a zero sum two monotone operators in real Hilbert space. Our proposed methods only require one forward evaluation single-valued operator backward set-valued at each iteration; feature that is absent many other available literature. We also develop ...

We consider an abstract second order non-autonomous evolution equation in a Hilbert space H : u ″ + Au γ ( t ) ′ f = 0, where A is self-adjoint and nonnegative operator on , conservative -valued function with polynomial growth (not necessarily to be monotone), time-dependent damping term. How exactly the decay of energy affected by coefficient exponent associated nonlinear term ? There seems li...

Abstract The primary goal of this research is to investigate the approximate numerical solution variational inequalities using quasimonotone operators in infinite-dimensional real Hilbert spaces. In study, sequence obtained by proposed iterative technique for solving converges strongly toward a due viscosity-type scheme. Furthermore, new that uses an inertial mechanism obtain strong convergence...

We investigate the complexity of finding prime implicants and minimum equivalent DNFs for Boolean formulas, and of testing equivalence and isomorphism of monotone formulas. For DNF related problems, the complexity of the monotone case differs strongly from the arbitrary case. We show that it is DP-complete to check whether a monomial is a prime implicant for an arbitrary formula, but the equiva...

We investigate the complexity of finding prime implicants and minimal equivalent DNFs for Boolean formulas, and of testing equivalence and isomorphism of monotone formulas. For DNF related problems, the complexity of the monotone case strongly differs from the arbitrary case. We show that it is DP-complete to check whether a monomial is a prime implicant for an arbitrary formula, but checking p...

We introduce an iterative method for finding a common element of set of fixed points of nonexpansive mappings, the set of solutions of a finite family of variational inclusion with setvalued maximal monotone mappings and inverse strongly monotone mappings, and the set of solutions of a mixed equilibrium problem in Hilbert spaces. Under suitable conditions, some strong convergence theorems for a...

In this paper we review various numerical homogenization methods for monotone parabolic problems with multiple scales. The spatial discretisation is based on finite element methods and the multiscale strategy relies on the heterogeneous multiscale method. The time discretization is performed by several classes of Runge-Kutta methods (strongly A−stable or explicit stabilized methods). We discuss...

In this paper, we continue to investigate the inexact hybrid proximal point algorithm proposed by Mashreghi and Nasri for equilibrium problems in Banach spaces. Under some classes of generalized monotone conditions, we prove that the sequence generated by the method is strongly convergent to a solution of the problem, which is closest to the initial iterate, in the sense of Bregman distance. As...

We introduce a new iterative scheme by shrinking projection method for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of common solutions of variational inclusion problems with set-valued maximal monotone mappings and inverse-strongly monotone mappings, the set of solutions of fixed points for nonexpansive semigroups, and the set of common fi...