We first prove the existence of solutions for a generalized mixed equilibrium problem under the new conditions imposed on the given bifunction and introduce the algorithm for solving a common element in the solution set of a generalized mixed equilibrium problem and the common fixed point set of finite family of asymptotically nonexpansivemappings. Next, the strong convergence theorems are obta...

This paper aims at establishing the existence of results for a nonstandard equilibrium problems $(EP_{N})$. The solutions of this inequality are discussed in a subset $K$ (either bounded or unbounded) of a Banach spaces $X$. Moreover, we enhance the main results by application of some differential inclusion.

The preference of a concave nontransitive consumer is represented by a skew-symmetric and concave-convex bifunction on the set of all commodity bundles. This paper characterizes finite sets of demand observations that are consistent with the demand behavior of such kind of consumer by a generalized monotonicity property.

In this paper we propose an inexact proximal point method to solve equilibrium problem using proximal distances and the diagonal subdifferential. Under some natural assumptions on the problem and the quasimonotonicity condition on the bifunction, we prove that the sequence generated for the method converges to a solution point of the problem.

An effective theranostic platform based on porous silica nanoparticles encapsulated with the complex of a photodynamic anticancer drug and graphene quantum dots (GQDs), with the bifunction of multicolor imaging and satisfactory photo-induced anticancer activity, was successfully designed and prepared for in vitro photodynamic therapy (PDT) of superficial cancer.

The paper deals with special types of $L$-ordered sets, $L$-fuzzy complete lattices, and fuzzy directed complete posets.First, a theorem for constructing monotone maps is proved, a characterization for monotone maps on an $L$-fuzzy complete lattice is obtained, and it's proved that if $f$ is a monotone map on an $L$-fuzzy complete lattice $(P;e)$, then the least fixpoint of $f$ is meet of a spe...

Equilibrium problems are articulated in a variety of mathematical computing applications, including minimax and numerical programming, saddle-point problems, fixed-point variational inequalities. In this paper, we introduce improved iterative techniques for evaluating the solution an equilibrium problem Hilbert space with pseudomonotone Lipschitz-type bifunction. These based on two steps proxim...

We discuss the equilibrium problem for a continuous bifunction over the fixed point set of a firmly nonexpansive mapping. We then present an iterative algorithm, which uses the firmly nonexpansive mapping at each iteration, for solving the problem. The algorithm is quite simple and it does not require monotonicity and Lipschitz-type condition on the equilibrium function. At the end of the paper...