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A mapping f : V n → W, where V is a commutative semi-group, W is a linear space and n is a positive integer, is called multi-additive if it is additive in each variable. In this paper we prove the Hyers-Ulam stability of multi-additive mappings in 2-Banach spaces. The corollaries from our main results correct some outcomes from [W.-G. Park, Approximate additive mappings in 2-Banach spaces and related topics, J. Math. Anal. Appl. 376 (2011) 193–202]. [ABSTRACT FROM AUTHOR]

The article presents a case study of a 73-year-old woman who was referred at the Lublin Medical University in Lublin, Poland due to pain and abdominal distension for three months along with a motoric dysphasia. She showed a coexistence of adult-type granulosa cell tumor in one of her ovaries with ovarian fibroma in the other. She was affected simultaneously with Meigs' syndrome and endometrial hyperplasia. The article also discusses the various symptoms of the said disease.

We investigate the existence and uniqueness of solutions of the functional equation , , where are closed intervals, and , are some continuous piecewise monotone functions. A fixed point principle plays a crucial role in the proof of our main result.

Background: The expression of p53 has been studied not only in primary human ovarian carcinomas, but also in borderline ovarian tumors, however, the results were discordant. Expression patterns of proteins involved in cell proliferation and apoptosis have been investigated in various human neoplasms, including female genital tract neoplasms., Objective: The aim of this investigation was to assess the staining pattern and immunolocalization of p53 and selected proliferative markers (Ki-67, MCM3, PCNA, and topoisomerase IIα) in borderline ovarian tumors (BOTs)., Design: The study group consisted of 42 women who underwent pelvic surgery between 2006-2015. The median patients' age was 46 years. The immunoperoxidase technique was employed using antibodies against p53, Ki-67, MCM3, PCNA, and topoisomerase IIα., Results: For p53, nuclear expression was observed in BOTs, however, cytoplasmatic immunoreactivity was also detected. Altogether, 25 (60%) tumors demonstrated positive p53 immunostaining, including overexpression found in 6 (14%). There were no significant differences in p53 expression between subgroups of clinicopathological variables. Immunoexpression of Ki-67, MCM3, PCNA, and topoisomerase IIα was nuclear. Ki-67 expression was positive in 12 (29%) cases and there was a trend towards a relationship between patients' age and Ki-67 staining (P=0.08). Interestingly, a significantly higher Ki-67 expression was found in tumors of ≥10 cm in diameter compared to smaller tumors (P=0.008). MCM3 expression was detected in 38 (90%) tumors, and PCNA expression in 28 (67%), yet none of clinicopathological factors was related to them. Topoisomerase IIα expression was present in 14 (33%) cases and, interestingly, its significantly higher expression was observed in BOTs of ≥10 cm in diameter compared to smaller tumors (P=0.008). Moreover, Spearman's correlation revealed highly significant positive associations between Ki-67 and topoisomerase IIα (R=0.403, P=0.008) and Ki-67 and MCM3 (R=0.469, P=0.001)., Conclusions: We report a high positive immunostaining rate for p53, suggesting a role of TP53 alterations in the development of BOTs in humans. The new finding of higher topoisomerase IIα immunostaining positivity in BOTs of ≥10 cm may be clinically relevant and requires further studies on larger patient groups.