When k(x,Y) "<.is~a quasi-monotone function a.'1d the random variables X and Y have fixed distributions, it is sho1~ under some further mild conditions that Ek(X,Y) is a monotone functional of the joint distribution function of X and Y. Its infimum and supremum are both attained and correspond to explicitly described joint distribution functions. * Research supported by the Air Force Office of ...

We introduce a hybrid iterative scheme for finding a common element of the set of solutions for a system of mixed equilibrium problems, the set of common fixed point for nonexpansive semigroup, and the set of solutions of the quasi-variational inclusion problem with multivalued maximal monotone mappings and inverse-strongly monotone mappings in Hilbert space. Under suitable conditions, some str...

The fact that a continuous monotone function is differentiable almost everywhere was established by Lebesgue in 1904. Riesz gave a completely elementary proof of this theorem in 1932 by using his ’Rising Sun Lemma’. Other than Riesz’s, all the proofs of this theorem utilize measure theory. Also a geometric proof which involves measure theory and sets of measure zero was given by D. Austin. The ...

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...

In this paper, we consider the numerical solution for the discretization of semilinear elliptic complementarity problems. A monotone algorithm is established based on the upper and lower solutions of the problem. It is proved that iterates, generated by the algorithm, are a pair of upper and lower solution iterates and converge monotonically from above and below, respectively, to the solution o...

We prove the existence of fixed points of monotone quasi-contraction mappings in metric and modular metric spaces. This is the extension of Ran and Reurings fixed point theorem for monotone contraction mappings in partially ordered metric spaces to the case of quasicontraction mappings introduced by Ćirić. The proofs are based on Lemmas ?? and ??, which contain two crucial inequalities essentia...

we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}...

We use the monotone iterative technique with upper and lower solutions in reversed order to obtain two monotone sequences that converge uniformly to extremal solutions of second order periodic boundary value problems and periodic solutions of functional differential equations(FDEs).

In this article, we investigate sufficient conditions for existence of maximal and minimal solutions to a coupled system of highly nonlinear differential equations of fractional order with mixed type boundary conditions. To achieve this goal, we apply monotone iterative technique together with the method of upper and lower solutions. Also an error estimation is given to check the accuracy of th...