An equivalent condition to the Jensen inequality for the generalized Sugeno integral.

For the classical Jensen inequality of convex functions, i.e., [Formula: see text] an equivalent condition is proved in the framework of the generalized Sugeno integral. Also, the necessary and sufficient conditions for the validity of the discrete form of the Jensen inequality for the generalized Sugeno integral are given

Hadamard Integral Inequality for the Class of Geodesic Convex Functions

In this paper, we introduce the concept of (γ,η)-convex function by the inequality fγx,y(t)≤ηf(x),f(y)(t), in which γ and η are two geodesic arcs. Then, we will find some refinements of Hadamard integral inequality for (γ,η)-convex functions in the case of Lebesgue and Sugeno integral

An equivalent condition to the Jensen inequality for the generalized Sugeno integral.

For the classical Jensen inequality of convex functions, i.e., [Formula: see text] an equivalent condition is proved in the framework of the generalized Sugeno integral. Also, the necessary and sufficient conditions for the validity of the discrete form of the Jensen inequality for the generalized Sugeno integral are given

An equivalent condition to the Jensen inequality for the generalized Sugeno integral

Abstract For the classical Jensen inequality of convex functions, i.e., H ( 1 μ ( D ) ∫ D f d μ ) ≤ 1 μ ( D ) ∫ D H ∘ f d μ , $$\begin{aligned} H \biggl(\frac{1}{\mu(D)} \int_{D}f\,d\mu \biggr)\leq\frac{1}{\mu (D)} \int_{D} H\circ f\,d\mu, \end{aligned}$$ an equivalent condition is proved in the framework of the generalized Sugeno integral. Also, the necessary and sufficient conditions for the validity of the discrete form of the Jensen inequality for the generalized Sugeno integral are given

Translation, validation and psychometric evaluation of the Persian (Farsi) version of the Low Anterior Resection Syndrome Score (LARS-P).

IntroductionLow anterior resection (LAR) for rectal cancer affects bowel function after the operation, causing a group of symptoms known as LAR Syndrome (LARS). LARS score is a patient-reported questionnaire to assess bowel dysfunction after the LAR operation. This study performed to validate the Persian (Farsi) translation of the LARS score and to investigate the psychometric properties of the score. The impact of LARS on the Quality of Life (QoL) of patients was also assessed.Materials and methodsThe LARS score was translated into Persian. Participants with a history of rectal cancer and low anterior resection were asked to complete the LARS score questionnaire. They were also asked a single question evaluating the impact of bowel function on QoL. Discriminative validity, convergent validity, sensitivity, and specificity of the questionnaire were calculated. A group of patients completed the score twice to assess the reliability of the questionnaire.ResultsFrom 358 patients with rectal cancer, 101 participants completed the Persian questionnaire. Answers of a high fraction of participants showed a moderate/perfect fit between their LARS score and their QoL. The Persian score demonstrated good convergent validity. It was able to differentiate between participants in terms of gender and T staging of the primary tumor. The score had high reliability.ConclusionThe Persian translation of the LARS score has excellent psychometric properties compared to previous translations in other languages. Therefore, it is a valid and reliable questionnaire to assess LARS