We introduce an iterative sequence for finding a common element of the set of fixed points of a nonexpansive mapping and the solutions of the variational inequality problem for three inversestrongly monotone mappings. Under suitable conditions, some strong convergence theorems for approximating a common element of the above two sets are obtained. Moreover, using the above theorem, we also apply...

In this paper, by combining a modified extragradient scheme with the viscosity approximation technique, an iterative scheme is developed for computing the common element of the set of fixed points of a sequence of asymptotically nonexpansive mappings and the set of solutions of the variational inequality problem for an α-inverse strongly monotone mapping. We prove a strong convergence theorem f...

Fixed point results for a self-map satisfying locally contractive conditions on a closed ball in an ordered 0-complete quasi-partial metric space have been established. Instead of monotone mapping, the notion of dominated mappings is applied. We have used weaker metric, weaker contractive conditions, and weaker restrictions to obtain unique fixed points. An example is given which shows that how...

*Correspondence: [email protected] 1Department of Mathematics, Faculty of Science For Girls, King Abdulaziz University, Jeddah, 21593, Saudi Arabia Full list of author information is available at the end of the article Abstract Let (X ,‖ · ‖) be a Banach space. Let C be a nonempty, bounded, closed, and convex subset of X and T : C→ C be a monotone nonexpansive mapping. In this paper, it is ...

A predicative semantics is a mapping of programs to predicates These pred icates characterize sets of acceptable observations The presence of time in the observations makes the obvious weakest xed point semantics of itera tive constructs unacceptable This paper proposes an alternative We will see that this alternative semantics is monotone and implementable feasible Fi nally a programming theor...

Differential equations of the type ∂ttu − ∇ · a(∇∂tu) − ∆u = f are studied, where the nonlinear mapping a is continuous, monotone and satisfies a coercivity condition in terms of a (generalised) N -function. The class of problems thus includes the case of anisotropic and nonpolynomial growth. Global existence of solutions in the sense of distributions is shown via convergence of the backward Eu...

We introduce a new iterative method for finding a common element of the set of solutions of a generalized equilibrium problem with a relaxed monotone mapping and the set of common fixed points of a countable family of nonexpansive mappings in a Hilbert space and then prove that the sequence converges strongly to a common element of the two sets. Using this result, we prove several new strong co...

In this paper, we introduce and study a new system of variational inclusions with B-monotone operators in Banach spaces. By using the proximal mapping associated with Bmonotone operator, we construct a new iterative algorithm for approximating the solution of this system of variational inclusions. We also prove the existence of solutions and the convergence of the sequences generated by the alg...

We show that the general variational inequalities are equivalent to the general WienerHopf equations and use this alterative equivalence to suggest and analyze a new iterative method for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the general variational inequality involving multivalued relaxed monotone operators. Our results impro...

In this work, it is presented iterative schemes for achieving to common points of the solutions set of the system of generalized mixed equilibrium problems, solutions set of the variational inequality for an inverse-strongly monotone operator, common fixed points set of two infinite sequences of relatively nonexpansive mappings and common zero points set of two finite sequences of maximal monot...