In this paper we use basic properties of strongly convex functions to obtain new inequalities including Jensen type and Jensen-Mercer type inequalities. Applications for special means are pointed out as well. We also give a Jensen's operator inequality for strongly convex functions. As a corollary, we improve the Hölder-McCarthy inequality under suitable conditions.
More precisely we show that iffor each positive operator A and x ∈ H with x = 1.2010 Mathematics Subject Classification. Primary 47A63, 26B25. Secondary 46L05.
Working in hot and humid environments can jeopardize the health and safety of the workers and reduce their efficiency. Different physical, environmental, and human factors can influence the risk level of working in these atmospheres. Therefore, the risk assessment of such atmospheres must be carried out from a holistic point of view. This paper aims to introduce a novel risk assessment and prioritization model, using hybrid AHP and VIKOR methods in a fuzzy environment. The AHP method was adopted to determine the importance (weight) of the risk influencing parameters. Also, the VIKOR as a compromise solution method was applied to rank the different working stations against the risk criteria. Fuzzy set theory was used to handle the inherent ambiguity and vagueness of the data encountered in the evaluation process. Furthermore, the fuzzy TOPSIS was adopted to further represent the efficacy of the proposed model. To demonstrate the applicability of the model, a small size foundry shop was selected as the real case and a sensitivity analysis was performed to confirm the validity of the model. The results revealed that the ''Environment'' has the most contribution to the risk level of hot environments (W E = 0.615). That is followed by ''Temperature'' (W DBT = 0.268), ''Air velocity'' (W AV = 0.170), ''Safety training'' (W ST = 0.161), ''Mean radiant intensity'' (W MRT = 0.110), ''Humidity'' (W H = 0.066), ''Seniority structure'' (W SS = 0.063), ''Work intensity'' (W WI = 0.058), ''PPE'' (W PPE = 0.047), ''Work nature'' (W PPE = 0.034), and '' Work duration'' (W T = 0.022), in sub-factors. Using the F-VIKOR method, the ''melting furnace'' workstation was determined as the compromise solution with the index value of Q = 1.
Abstract. New upper and lower bounds for the numerical radii of Hilbert space operators are given. Among our results, we prove that if A ∈ B (H ) is a hyponormal operator, then for all non-negative non-decreasing operator convex f on [0,∞), we have
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