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In this paper, we present a new iteration method for solving monotone equilibrium problems. This new method is based on the ergodic iteration method Ronald and Bruck in (J Math Anal Appl 61:159-164, 1977) and the auxiliary problem principle Noor in (J Optim Theory Appl 122:371-386, 2004), but it includes the usage of symmetric and positive definite matrices. The proposed algorithm is very simple. Moreover, it simplifies the assumptions necessary in order to converge to the solution. Specifically, whereas previous methods require strong monotonicity and Lipschitz-type continuous conditions, our proposed method only requires weak monotonicity conditions. Applications to the generalized variational inequality problem and some numerical results are reported.

Auricular reconstruction is a unique area of facial plastic surgery where a wide array of reconstructive options often must be considered. The external ear is unique in its aesthetic role where the normal auricle often goes unnoticed; yet even a small irregularity can stand out and become conspicuous. The reconstruction of large or total auricular defects is a combination of science and art. Two forms of auricular reconstruction are discussed: (1) those for a congenitally abnormal shape but no acquired tissue deficiency, that is, otoplasty, and (2) repairs requiring a reconstruction of discrete loss of tissue. A general algorithm is presented that can assist with flap selection and covers the techniques for grafts, framework repair, local and pedicled flaps, temporoparietal facial flaps, and auricular prostheses.

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Upper blepharoplasty is one of the more common facial plastic procedures. The upper lid and brow complex are managed together. Whether upper blepharoplasty is performed for medical or cosmetic reasons, the aim is to improve appearance while retaining natural shape and maintaining (or improving) function. For optimal results, it is important to understand relevant eyelid anatomy and the concept of maintaining youthful volume and position of the eyelid brow orbit complex. Management of patient expectations, meticulous planning, and a degree of surgical finesse all contribute to the desired outcome. The article will focus on the assessment, techniques, and complications of upper blepharoplasty, which involve management of the skin, orbicularis oculi, preaponeurotic fat, levator aponeurosis and muscle as related to concomitant ptosis, and lateral brow complex via transblepharoplasty (internal) brow lift and fixation.