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Abstract: In this paper, we introduce hybrid pseudoviscosity approximation schemes with strongly positive bounded linear operators for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points of infinitely many nonexpansive mappings in the setting of Hilbert spaces. We prove the strong convergence of the sequences generated by our scheme to a solution of an equilibrium problem which is also a common fixed point of infinitely many nonexpansive mappings. Our results can be treated as extension and improvement of the corresponding results appeared in the literature in the recent past. [Copyright &y& Elsevier]

Abstract: By constructing some suitable examples, Jeyakumar and Yen (2004)  have shown that the Robinson metric regularity (Rmr) and the Lipschitz-like property (Llp) of implicit multifunctions are not equivalent. This paper clarifies relationships between the two properties of implicit multifunctions. It turns out that the (reasonable) sufficient conditions for having (Rmr) (Llp) are quite different from those for the validity of the reverse implication. The implicit function theorem due to Yen and Yao (2009) serves as a tool for our analysis of (Rmr) and (Llp). [Copyright &y& Elsevier]

Abstract: We obtain some point-based sufficient conditions for the metric regularity in Robinson’s sense of implicit multifunctions in a finite-dimensional setting. The new implicit function theorem (which is very different from the preceding results of Ledyaev and Zhu [Yu.S. Ledyaev, Q.J. Zhu, Implicit multifunctions theorems, Set-Valued Anal. 7 (1999) 209–238], Ngai and Théra [H.V. Ngai, M. Théra, Error bounds and implicit multifunction theorem in smooth Banach spaces and applications to optimization, Set-Valued Anal. 12 (2004) 195–223], Lee, Tam and Yen [G.M. Lee, N.N. Tam, N.D. Yen, Normal coderivative for multifunctions and implicit function theorems, J. Math. Anal. Appl. 338 (2008) 11–22]) can be used for analyzing parametric constraint systems as well as parametric variational systems. Our main tools are the concept of normal coderivative due to Mordukhovich and the corresponding theory of generalized differentiation. [Copyright &y& Elsevier]

Abstract: Let be a reflexive and smooth real Banach space which has a weakly sequentially continuous duality mapping. In this paper, we consider the following viscosity approximation scheme (where is a generalized contraction mapping) for infinitely many nonexpansive self-mappings in . We establish a strong convergence result which generalizes some results in the literature. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to introduce and analyze an extragradient method with regularization for finding a common element of the solution set of the split feasibility problem and the set of fixed points of a nonexpansive mapping in the setting of infinite-dimensional Hilbert spaces. Combining the regularization method and the extragradient method due to Nadezhkina and Takahashi [N. Nadezhkina, W. Takahashi, Weak convergence theorem by an extragradient method for nonexpansive mappings and monotone mappings, J. Optim. Theory Appl. 128 (2006) 191–201], we propose an iterative algorithm for finding an element of . We prove that the sequences generated by the proposed algorithm converge weakly to an element of under mild conditions. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the split feasibility problem (SFP) in infinite-dimensional Hilbert spaces, and study the relaxed extragradient methods for finding a common element of the solution set of SFP and the set of fixed points of a nonexpansive mapping . Combining Mann’s iterative method and Korpelevich’s extragradient method, we propose two iterative algorithms for finding an element of . On one hand, for , the identity mapping, we derive the strong convergence of one iterative algorithm to the minimum-norm solution of the SFP under appropriate conditions. On the other hand, we also derive the weak convergence of another iterative algorithm to an element of under mild assumptions. [Copyright &y& Elsevier]

Abstract: The present paper is divided into two parts. In the first part, we introduce implicit and explicit iterative schemes for finding the fixed point of a nonexpansive mapping defined on the closed convex subset of a real Hilbert space. We establish results on the strong convergence of the sequences generated by the proposed schemes to a fixed point of a nonexpansive mapping. Such a fixed point is also a solution of a variational inequality defined on the set of fixed points. In the second part, we propose implicit and explicit iterative schemes for finding the approximate minimizer of a constrained convex minimization problem and prove that the sequences generated by our schemes converge strongly to a solution of the constrained convex minimization problem. Such a solution is also a solution of a variational inequality defined over the set of fixed points of a nonexpansive mapping. The results of this paper extend and improve several results presented in the literature in the recent past. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce the concept of a -function defined on a quasi-metric space which generalizes the notion of a -function and a -distance. We establish Ekeland-type variational principles in the setting of quasi-metric spaces with a -function. We also present an equilibrium version of the Ekeland-type variational principle in the setting of quasi-metric spaces with a -function. We prove some equivalences of our variational principles with Caristi–Kirk type fixed point theorems for multivalued maps, the Takahashi minimization theorem and some other related results. As applications of our results, we derive existence results for solutions of equilibrium problems and fixed point theorems for multivalued maps. We also extend the Nadler’s fixed point theorem for multivalued maps to a -function and in the setting of complete quasi-metric spaces. As a consequence, we prove the Banach contraction theorem for a -function and in the setting of complete quasi-metric spaces. The results of this paper extend and generalize many results appearing recently in the literature. [Copyright &y& Elsevier]

Background: In the phase 3 RADIANT-2 study, everolimus plus octreotide long-acting repeatable (LAR) showed improvement of 5.1months in median progression-free survival versus placebo plus octreotide LAR among patients with advanced neuroendocrine tumors associated with carcinoid syndrome. The progression-free survival P-value was marginally above the prespecified threshold for statistical significance. Here, we report final overall survival (OS) and key safety update from RADIANT-2. Patients and methods: The RADIANT-2 trial compared everolimus (10 mg/day, orally; n=216) versus placebo (n=213), both in conjunction with octreotide LAR (30 mg, intramuscularly, every 28 days). Patients, unblinded at the time of progression or after end of double-blind core phase following primary analysis, were offered open-label everolimus with octreotide LAR (openlabel phase). In the open-label phase, patients had similar safety and efficacy assessments as those in the core phase. For OS, hazard ratios (HRs) with 95% CIs using unadjusted Cox model and a Cox model adjusted for prespecified baseline covariates were calculated. Results: A total of 170 patients received open-label everolimus (143 crossed over from the placebo arm; 27 in the everolimus arm continued to receive the same treatment after unblinding). The median OS (95% CI) after 271 events was 29.2 months (23.8-35.9) for the everolimus arm and 35.2 months (30.0-44.7) for the placebo arm (HR, 1.17; 95% CI, 0.92-1.49). HR adjusted for baseline covariates was 1.08 (95% CI, 0.84-1.38). The most frequent drug-related grade 3 or 4 AEs reported during the openlabel phase were diarrhea (5.3%), fatigue (4.7%) and stomatitis (4.1%). Deaths related to pulmonary or cardiac failure were observed more frequently in the everolimus arm. Conclusion: No significant difference in OS was observed for the everolimus plus octreotide LAR and placebo plus octreotide LAR arms of the RADIANT-2 study, even after adjusting for imbalances in the baseline covariates. [ABSTRACT FROM AUTHOR]

Background: Incidence of locoregional neuroendocrine tumors (NETs) is rising. However, after curative resection, the patterns and risk factors associated with recurrence remain unknown. Consensus guidelines recommend surveillance every 6-12 months for up to 10 years after surgery for resected, well-differentiated NETs irrespective of patient demographics, site, grade or stage of tumor with few exceptions. Patients and methods: From the Surveillance, Epidemiology and End Results (SEER)-Medicare database, we identified localized and regional stage NET patients who underwent surgical resection between January 2002 and December 2011. Development of recurrence was identified by capturing at least two claims indicative ofmetastatic disease until 31 December 2013. Results: Of the 2366 identified patients (median age 73 years), 369 (16%) developed metastatic disease within 5 years and only an additional 1% developed metastases between years 5 and 10 with the majority dying due to unrelated causes. The 5-year risk of developing metastases (hazard ratio, HR) varied significantly (log-rank P<0.001) by grade: 9.9% versus 25.9% (2.2) versus 48.1% (4.4) for grades 1, 2 and ⩾3, respectively; stage: 10.3% versus 31.1% (2.8) for localized versus regional; primary tumor size: 7.6% versus 15% (1.3) versus 26.6% (1.5) for<1, 1-2 and>2 cm, respectively and site: ranging from 11.3% for colon to 23.9% for pancreas. Conclusions: Contrary to current guidelines, our study suggests that surveillance recommendations should be tailored according to patient and tumor characteristics. Surveillance past 5 years may be avoided in elderly patients with competing morbidities or low risk of recurrence. Pancreatic, lung, higher grade and regional NETs have a higher risk of recurrence and may be considered for future adjuvant trials. [ABSTRACT FROM AUTHOR]

Background: Several studies have demonstrated the antitumor activity of first-generation somatostatin analogs (SSAs), primarily targeting somatostatin receptor (sstr) subtypes 2 and 5, in neuroendocrine tumors (NET). Pasireotide, a second-generation SSA, targets multiple sstr subtypes. We compared the efficacy and safety of pasireotide plus everolimus to everolimus alone in patients with advanced, well-differentiated, progressive pancreatic NET. Patients and methods: Patients were randomized 1 : 1 to receive a combination of everolimus (10 mg/day, orally) and pasireotide long-acting release (60 mg/28 days, intramuscularly) or everolimus alone (10 mg/day, orally); stratified by prior SSA use, and baseline serum chromogranin A and neuron-specific enolase. The primary end point was progression-free survival (PFS). Secondary end points included overall survival, objective response rate, disease control rate, and safety. Biomarker response was evaluated in an exploratory analysis. Results: Of 160 patients enrolled, 79 were randomized to the combination arm and 81 to the everolimus arm. Baseline demographics and disease characteristics were similar between the treatment arms. No significant difference was observed in PFS: 16.8months in combination arm versus 16.6months in everolimus arm (hazard ratio, 0.99; 95% confidence interval, 0.64-1.54). Partial responses were observed in 20.3% versus 6.2% of patients in combination arm versus everolimus arm; however, overall disease control rate was similar (77.2% versus 82.7%, respectively). No significant improvement was observed inmedian overall survival. Adverse events were consistent with the known safety profile of both the drugs; grade 3 or 4 fasting hyperglycemia was seen in 37% versus 11% of patients, respectively. Conclusions: The addition of pasireotide to everolimus was not associated with the improvement in PFS compared with everolimus alone in this study. Further studies to delineate mechanisms by which SSAs slow tumor growth in NET are warranted. [ABSTRACT FROM AUTHOR]

Background The contribution of induction chemotherapy (IC) before preoperative chemoradiation for esophageal cancer (EC) is not known. We hypothesized that IC would increase the rate of pathologic complete response (pathCR). Methods Trimodality-eligibile patients were randomized to receive no IC (Arm A) or IC (oxaliplatin/FU; Arm B) before oxaliplatin/FU/radiation. Surgery was attempted ∼5–6 weeks after chemoradiation. The pathCR rate, post-surgery 30-day mortality, overall survival (OS), and toxic effects were assessed. Bayesian methods and Fisher's exact test were used. Results One hundred twenty-six patients were randomized dynamically to balance the two arms for histology, baseline stage, gender, race, and age. Fifty-five patients in Arm A and 54 in Arm B underwent surgery. The median actuarial OS for all patients (54 deaths) was 45.62 months [95% confidence interval (CI), 27.63–NA], with median OS 45.62 months (95% CI 25.56–NA) in Arm A and 43.68 months (95% CI 27.63–NA) in Arm B (P = 0.69). The pathCR rate in Arm A was 13% (7 of 55) and 26% (14 of 54) in Arm B (two-sided Fisher's exact test, P = 0.094). Safety was similar in both arms. Conclusions These data suggest that IC produces non-significant increase in the pathCR rate and does not prolong OS. Further development of IC before chemoradiation may not be beneficial. [ABSTRACT FROM PUBLISHER]

Abstract: We introduce a new composite iterative scheme to approximate a zero of an -accretive operator defined on uniform smooth Banach spaces and a reflexive Banach space having a weakly continuous duality map. It is shown that the iterative process in each case converges strongly to a zero of . The results presented in this paper substantially improve and extend the results due to Ceng et al. [L.C. Ceng, H.K. Xu, J.C. Yao, Strong convergence of a hybrid viscosity approximation method with perturbed mappings for nonexpansive and accretive operators, Taiwanese J. Math. (in press)], Kim and Xu [T.H. Kim, H.K. Xu, Strong convergence of modified Mann iterations, Nonlinear Anal. 61 (2005) 51–60] and Xu [H.K. Xu, Strong convergence of an iterative method for nonexpansive and accretive operators, J. Math. Anal. Appl. 314 (2006) 631–643]. Our work provides a new approach for the construction of a zero of -accretive operators. [Copyright &y& Elsevier]