A fixed point theoremfor nonexpansive compact self-mapping

A mapping T from a topological space X to a topological space Y is said to be compact if T(X) is contained in a compact subset of Y . The aim of this paper is to prove the existence of fixed points of a nonexpansive compact self-mapping defined on a closed subset having a contractive jointly continuous family when the underlying space is a metric space. The proved result generalizes and extends several known results on the subject

Some Fixed Point Theorems for Kannan Mappings

2000 Mathematics Subject Classification: Primary: 47H10; Secondary: 54H25.Some results on the existence and uniqueness of fixed points for Kannan mappings on admissible subsets of bounded metric spaces and on bounded closed convex subsets of complete convex metric spaces having uniform normal structure are proved in this paper. These results extend and generalize some results of Ismat Beg and Akbar Azam [Ind. J. Pure Appl. Math. 18 (1987), 594-596], A. A. Gillespie and B. B. Williams [J. Math. Anal. Appl. 74 (1980), 382-387] and of Yoichi Kijima and Wataru Takahashi [Kodai Math Sem. Rep. 21 (1969), 326-330]

Metrically Round and Sleek Metric Spaces

A round metric space is the one in which closure of each open ball is the corresponding closed ball. By a sleek metric space, we mean a metric space in which interior of each closed ball is the corresponding open ball. In this, article we establish some results on round metric spaces and sleek metric spaces.Comment: 13 pages, 10 Figure

On strong proximinality in normed linear spaces

The paper deals with strong proximinality in normed linear spaces. It is proved that in  a compactly locally uniformly rotund Banach space, proximinality, strong proximinality, weak approximative compactness and  approximative compactness are all equivalent for closed convex sets. How strong proximinality can be transmitted to and from quotient spaces has also been discussed

Round and sleek subspaces of linear metric spaces and metric spaces

In the recent work [Metrically round and sleek metric spaces, \emph{The Journal of Analysis} (2022), pp 1--17], the authors proved some results on metrically round and sleek linear metric spaces and metric spaces. In continuation, the present article discusses more results on such spaces along with identification of round and sleek subsets of linear metric spaces and metric spaces in the subspace topology.Comment: 14 pages, 1figur

Meat Consumption and Risk of Developing Esophageal Cancer: A Meta-analysis

Background: Meat has been linked as a risk factor for several cancers. Red meat and processed meat specifically have been suggested as risk factors for esophageal cancer, but this has not been established. We performed a meta-analysis to summarize available evidence from case-control and cohort studies on this topic.Methods: A systematic search of MEDLINE, PubMed, EMBASE was completed up until November, 2013. Studies were included that reported confirmed histological diagnosis of cancer, odds ratios (OR) or relative risks (RR) and confidence intervals (CI). Pooled ORs and 95% CIs were calculated for the effect of different meats on the development of esophageal cancer using a random effects model. Studies were assessed for heterogeneity and publication bias.Results: 29 studies were included in this analysis, involving 1,208,768 individuals with a total of 8,620 cases and 44,574 controls. High consumption rates were associated with development of cancer for red meat (OR 1.59; 95% CI 1.31-1.93), processed meat (OR 1.75; 95% CI 1.28-2.38), barbecued meat (OR 1.54; 95% CI 1.25–1.91) and overall (OR 1.26; 95% CI 1.11-1.43). Low and medium consumption rates were also significant for red and barbecued meat. High and medium consumption of white meat was significantly protective. High consumption of fish was also found to be protective (OR 0.73; 95% CI 0.55-0.95).Conclusions: Findings of this meta-analysis demonstrated red meat, processed meat and barbecued meat are likely to increase the risk of esophageal cancer in a dose dependent relationship. Fish and white meat were shown to have a protective effect

Fractures of the proximal humerus in children and adolescents

Background: In most children proximal humeral fractures are treated non-operatively with generally good results. The aim of the study was to evaluate the clinical outcome of closed/open reduction in children with severely displaced proximal humeral fractures. Materials and Methods: The charts of 15 patients (8 girls and 7 boys; mean age: 9.4 years) with proximal humeral fractures who were managed at our institution were reviewed from October 2011 to December 2013. Results: There were 7 metaphyseal fractures and 8 physeal injuries which were angulated according to Neer-Horowitz score as grade II (n=2), grade III(n=4) and grade IV(n=9). Associated lesions comprised open fracture with head trauma in a 2 year old female child which was operated on primarily and the 14 others by secondary intention. All patients were treated surgically with either closed (n = 5) or open (n=10) reduction and internal fixation with Kirschner wire or titanium elastic nails (TENs). They were assessed for clinical and radiological healing at a mean follow up of 1.25 years ranging from 0.5 to 2.0 years. Conclusion: Surgical option is indicated for severely displaced and unstable fractures in older children and adolescents. In addition to the periosteum , long head of the biceps, deltoid muscle, and bone fragments in combination can prevent fracture reduction. Key words: Proximal humerus fracture, Children, Open reduction, Operative