The purpose of this paper is to consider an iterative method for an equilibrium problem and a family relatively nonexpansive mappings. Weak convergence theorems are established in uniformly smooth and uniformly convex Banach spaces.

In optimal planning as heuristic search, admissible pruning techniques are paramount. One idea is dominance pruning, identifying states “better than” other states. Prior approaches are limited to simple dominance notions, like “more STRIPS facts true” or “higher resource supply”. We apply simulation, well-known in model checking, to compute much more general dominance relations based on compari...

In this paper, we introduce generalized cyclic φ-contraction maps in metric spaces and give some results of best proximity points of such mappings in the setting of a uniformly convex Banach space. Moreover, we obtain convergence and existence results of proximity points of the mappings on reflexive Banach spaces

In this paper, we present a new method for solving Reproducing Kernel Space (RKS) theory, and iterative algorithm for solving Generalized Burgers Equation (GBE) is presented. The analytical solution is shown in a series in a RKS, and the approximate solution u(x,t) is constructed by truncating the series. The convergence of u(x,t) to the analytical solution is also proved.

We investigate the convergence of Mann-type iterative scheme for a countable family of strict pseudocontractions in a uniformly convex Banach space with the Fréchet differentiable norm. Our results improve and extend the results obtained by Marino-Xu, Zhou, Osilike-Udomene, Zhang-Guo and the corresponding results. We also point out that the condition given by ChidumeShahzad 2010 is not satisfie...

We propose a family of gradient algorithms for minimizing a quadratic function f(x) = (Ax, x)/2− (x, y) in R or a Hilbert space, with simple rules for choosing the step-size at each iteration. We show that when the step-sizes are generated by a dynamical system with ergodic distribution having the arcsine density on a subinterval of the spectrum of A, the asymptotic rate of convergence of the a...

Technological advances in position aware devices increase the availability of tracking data of everyday objects such as animals, vehicles, people or football players. We propose a geographic data mining approach to detect generic aggregation patterns such as flocking behaviour and convergence in geospatial lifeline data. Our approach considers the object's motion properties in an analytical spa...

We present sufficient convergence conditions for two-step Newton methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. The advantages of our approach under the same computational cost over other studies such as [9–25] for the semilocal convergence case are: weaker sufficient convergence conditions, more precise error bounds on the distances...

begin{abstract} In this paper, we prove some strong and weak convergence of three step random iterative scheme with errors to common random fixed points of three asymptotically nonexpansive nonself random mappings in a real uniformly convex separable Banach space. end{abstract}