‎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...

a general notion of completely monotone functionals on an ordered banach algebra b into a proper h*-algebra a with an integral representation for such functionals is given. as an application of this result we have obtained a characterization for the generalized completely continuous monotone functions on weighted foundation semigroups. a generalized version of bochner’s theorem on foundation se...

The principal goal of this work is to investigate new sufficient conditions for the existence and convergence positive definite solutions certain classes matrix equations. Under specific assumptions, basic tool in our study a monotone mapping, which admits unique fixed point setting partially ordered Banach space. To estimate these equations, we use Krasnosel’skiĭ iterative technique. We also d...

The Method of Auxiliary Mapping (MAM), introduced by Babuška and Oh, was proven to be very successful in dealing with monotone singularities arising in two dimensional problems. In this paper, in the framework of the p-version of FEM, MAM is presented for one-dimensional elliptic boundary value problems containing singularities. Moreover, in order to show the effectiveness of MAM, a detailed pr...

We introduce a new hybrid iterative algorithm for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings, the set of solutions of the variational inequality of a monotone mapping, and the set of solutions of a mixed equilibrium problem. This study, proves a strong convergence theorem by the proposed hybrid iterative algorithm which solves fixed-point ...

In this paper, we introduce and analyze some generalized hybrid proximal point algorithms for finding a common element of the set of zeros of a maximal monotone operator and the set of fixed points of a nonexpansive mapping in a Hilbert space. These algorithms include the previously known proximal point algorithms as special cases. Weak and strong convergence of the proposed proximal point algo...

This article considers a parallel monotone hybrid algorithm for finite family of G-nonexpansive mapping in Hilbert spaces endowed with graphs and suggests iterative schemes finding common fixed point by the two different projection methods. Moreover, we show computational performance our comparison to some Strong convergence theorems are proved under suitable conditions. Finally, give numerical...

and Applied Analysis 3 to a fixed point of the mapping T , which is also a solution of VI 1.5 defined on the set of fixed points of T . As direct consequences, we obtain the unique minimum-norm fixed point of T . Namely, we find the unique solution of the quadratic minimization problem: ‖x̃‖ min{‖x‖ : x ∈ Fix T }. 2. Preliminaries and Lemmas Throughout this paper, when {xn} is a sequence inH, xn...

Variational inequalities with linear inequality constraints are widely used in constrained optimization and engineering problems. By extending a new recurrent neural network [14], this paper presents a recurrent neural network for solving variational inequalities with general linear constraints in real time. The proposed neural network has onelayer projection structure and is amenable to parall...

We investigate the following extendability problem for systems, for which the available information is given by a monotone set mapping M on the field CT of measurable cylinders of a product ample space (XT ,RT ): given that M is invariant under a RT −RT measurable transformation H of XT , i.e. M(H−1(B)) = M(B) for all B ∈ CT , is it possible to find H-invariant monotone extensions of M to the p...