The aim of this paper is to introduce a viscosity iterative algorithm for the implicit midpoint rule of nonexpansive mappings in uniformly smooth spaces. Under some appropriate conditions on the parameters, we prove some strong convergence theorems. As applications, we apply our main results to solving fixed point problems of strict pseudocontractive mappings, variational inequality problems in...

Given two conics over an infinite field that intersect at the origin, a line through the origin will, in general intersect both conic sections once more each, at points C and D. As the line varies we find that the midpoint of C and D traces out a curve, which is typically a quartic. Intuitively, this locus is the “average” of the two conics from the perspective of an observer at the origin. We ...

We propose a new version of potentially optimal intervals for the DIRECT algorithm. A two-points based sampling method is presented. The method starts from a distingished point (the peak point) by forming an initial triangle. The idea is to sample the midpoint of a specific interval: the basis of the resulting triangle. This specific interval is obtained by translating the initial interval towa...

In this paper the midpoint approach for efficient scan conversion of parabola on hexagonal grid is proposed. The mid-point approach computes pixel nearest true curve using only integer arithmetic. The proposed algorithm is compared favorably with the existing parabola drawing algorithm on square grid. Owing to this approach we may visualize design ideas through animations and photorealistic ren...

Abstract The present paper aims to find some new midpoint-type inequalities for twice quantum differentiable convex functions. consequences derived in this are unification and generalization of the comparable literature on midpoint inequalities.