Unpredictability of hip behavior in Dyggve-Melchior-Clausen syndrome: A mid-term assessment of siblings

SummaryDyggve-Melchior-Clausen syndrome is a rare spondylo-epiphyseal disease, which almost constantly leads to both bilateral hip degeneration and dislocation. Few authors have reported to date the surgical management of this orthopaedic disorder. We present two new cases affecting siblings. One brother was treated by unilateral triple pelvic osteotomy combined with varus osteotomy of the proximal femur; the other was treated by bilateral Pemberton osteotomies with varus osteotomy of the proximal femur. At a respective 5-year and 3-year follow-up delay, both cases had evolved towards progressive subluxation recurrence along with severe hip degeneration. Based on both our experience and literature review, it seems that one should avoid operating these hips unless pain renders surgery mandatory. Total hip arthroplasty seems the only reliable surgical solution at the adult age and paediatric surgeons should keep in mind that previous femoral osteotomies will make it more challenging for adult orthopaedic surgeons to implant on a remodeled anatomy

On some fixed point theorems under (α,ψ,ϕ) -contractivity conditions in metric spaces endowed with transitive binary relations

After the appearance of Nieto and Rodríguez-López’s theorem, the branch of fixed point theory devoted to the setting of partially ordered metric spaces have attracted much attention in the last years, especially when coupled, tripled, quadrupled and, in general, multidimensional fixed points are studied. Almost all papers in this direction have been forced to present two results assuming two different hypotheses: the involved mapping should be continuous or the metric framework should be regular. Both conditions seem to be different in nature because one of them refers to the mapping and the other one is assumed on the ambient space. In this paper, we unify such different conditions in a unique one. By introducing the notion of continuity of a mapping from a metric space into itself depending on a function α, which is the case that covers the partially ordered setting, we extend some very recent theorems involving control functions that only must be lower/upper semi-continuous from the right. Finally, we use metric spaces endowed with transitive binary relations rather than partial orders.This article was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah. N Shahzad acknowledges with thanks DSR for financial support. A-F Roldán-López-de-Hierro is grateful to the Department of Quantitative Methods for Economics and Business of the University of Granada. The same author has been partially supported by Junta de Andalucía by project FQM-268 of the Andalusian CICYE

Duplication of 10q24 locus: broadening the clinical and radiological spectrum

Split-hand-split-foot malformation (SHFM) is a rare condition that occurs in 1 in 8500-25,000 newborns and accounts for 15% of all limb reduction defects. SHFM is heterogeneous and can be isolated, associated with other malformations, or syndromic. The mode of inheritance is mostly autosomal dominant with incomplete penetrance, but can be X-linked or autosomal recessive. Seven loci are currently known: SHFM1 at 7q21.2q22.1 (DLX5 gene), SHFM2 at Xq26, SHFM3 at 10q24q25, SHFM4 at 3q27 (TP63 gene), SHFM5 at 2q31 and SHFM6 as a result of variants in WNT10B (chromosome 12q13). Duplications at 17p13.3 are seen in SHFM when isolated or associated with long bone deficiency. Tandem genomic duplications at chromosome 10q24 involving at least the DACTYLIN gene are associated with SHFM3. No point variant in any of the genes residing within the region has been identified so far, but duplication of exon 1 of the BTRC gene may explain the phenotype, with likely complex alterations of gene regulation mechanisms that would impair limb morphogenesis. We report on 32 new index cases identified by array-CGH and/or by qPCR, including some prenatal ones, leading to termination for the most severe. Twenty-two cases were presenting with SHFM and 7 with monodactyly only. Three had an overlapping phenotype. Additional findings were identified in 5 (renal dysplasia, cutis aplasia, hypogonadism and agenesis of corpus callosum with hydrocephalus). We present their clinical and radiological findings and review the literature on this rearrangement that seems to be one of the most frequent cause of SHFM

Hybrid Viscosity Approaches to General Systems of Variational Inequalities with Hierarchical Fixed Point Problem Constraints in Banach Spaces

The purpose of this paper is to introduce and analyze hybrid viscosity methods for a general system of variational inequalities (GSVI) with hierarchical fixed point problem constraint in the setting of real uniformly convex and 2-uniformly smooth Banach spaces. Here, the hybrid viscosity methods are based on Korpelevich’s extragradient method, viscosity approximation method, and hybrid steepest-descent method. We propose and consider hybrid implicit and explicit viscosity iterative algorithms for solving the GSVI with hierarchical fixed point problem constraint not only for a nonexpansive mapping but also for a countable family of nonexpansive mappings in X, respectively. We derive some strong convergence theorems under appropriate conditions. Our results extend, improve, supplement, and develop the recent results announced by many authors

One-local retract and common fixed point in modular function spaces

In this paper, we introduce and study the concept of one-local retract in modular function spaces. In particular, we prove that any commutative family of ρ-nonexpansive mappings defined on a nonempty, ρ-closed and ρ-bounded subset of a modular function space has a common fixed point provided its convexity structure of admissible subsets is compact and normal

Mann-Type Extragradient Methods for General Systems of Variational Inequalities with Multivalued Variational Inclusion Constraints in Banach Spaces

We introduce Mann-type extragradient methods for a general system of variational inequalities with solutions of a multivalued variational inclusion and common fixed points of a countable family of nonexpansive mappings in real smooth Banach spaces. Here the Mann-type extragradient methods are based on Korpelevich's extragradient method and Mann iteration method. We first consider and analyze a Mann-type extragradient algorithm in the setting of uniformly convex and 2-uniformly smooth Banach space and then another Mann-type extragradient algorithm in a smooth and uniformly convex Banach space. Under suitable assumptions, we derive some weak and strong convergence theorems. The results presented in this paper improve, extend, supplement, and develop the corresponding results announced in the earlier and very recent literature