In this paper, we introduce a general viscosity-type extragradient method for solving the fixed point problem of an asymptotically nonexpansive mapping and variational inclusion with two accretive operators. We obtain strong convergence theorem in setting Banach spaces. terms theorem, establish result (FPP) inequality (VIP) inverse-strongly monotone framework Hilbert Finally, is applied to deal...

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 prove necessary and sufficient conditions for locally Lipschitz Löwner operators to be monotone, strictly monotone and strongly monotone. Utilizing our characterization of the strict monotonicity of Löwner operators, we generalize Mangasarian class of Nonlinear Complementarity Problem (NCP)-functions to the setting of symmetric cone complementarity problem. This affirmatively answers a quest...

In this paper, the authors prove some existence results of solutions for a new class of generalized quasi-variational inequalities (GQVI) for pseudo-monotone type III operators and strongly pseudo-monotone type III operators defined on noncompact sets in locally convex Hausdorff topological vector spaces. In obtaining these results on GQVI for pseudo-monotone type III operators, we shall use Ch...

‎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 consider the primal problem of finding the zeros of the sum of a maximally monotone operator with the composition of another maximally monotone operator with a linear continuous operator and a corresponding dual problem formulated by means of the inverse operators. A primal-dual splitting algorithm which simultaneously solves the two problems in finite-dimensional spaces is presented. The sc...

We introduce an iterative procedure for finding a point in the zero set (a solution to 0 ∈ A(v) and v ∈ C) of an inverse-monotone or inverse strongly-monotone operator A on a nonempty closed convex subset C in a uniformly smooth and uniformly convex Banach space. We establish weak convergence results under suitable assumptions.