On the Jensen type inequality for generalized Sugeno integral

Converses of the Jensen inequality derived from the Green functions with applications in information theory

“…In the literature of inequalities, Jensen inequality is of pivotal importance because other classical inequalities, eg, Ky‐Fan, Hölder, Levinson's, Beckenbach‐Dresher, Minkowski's, arithmetic‐geometric, and Young's inequalities, can be deduced from this inequality. Also, this inequality has been applied to solve many problems in different fields of science and technology, eg, engineering, mathematical statistics, financial economics, and computer science, and an extensive literature exists regarding its generalizations, refinements, extensions, converses, etc …”

“…Also, this inequality has been applied to solve many problems in different fields of science and technology, eg, engineering, mathematical statistics, financial economics, and computer science, and an extensive literature exists regarding its generalizations, refinements, extensions, converses, etc. 3,[13][14][15][16][17][18][19][20][21][22][23][24][25] In the following theorem, Jensen integral inequality has been presented 26 :…”

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

“…Kaluszka et al [ 2 ] studied the Jensen inequality ( 1 ) for the generalized Sugeno integral by using the condition of monotonicity instead of the condition of convexity. The aim of this paper is to study the Jensen inequality for the generalized Sugeno integral without losing the condition of convexity.…”

On Carlson’s inequality for Sugeno and Choquet integrals

“…Since then, the fuzzy integral counterparts of several classical inequalities, including Chebyshev's, Jensen's, Minkowski's and Hölder's inequalities, are given by Flores-Franulič and Román-Flores [9], Agahi et al [2], L. Wu et al [35] and others. Furthermore many researchers started to study inequalities for the seminormed Sugeno integral [1,16,17,24].…”

“…Suppose f : X → [0, ∞), A ⊂ [0, ∞] and µ ∈ M such that µ(A ∪ B) µ(A) + µ(B) for A, B ∈ F . hf p dµ ,where H pq (a, b) is given by(17), p > 1 and 1/p + 1/q = 1.…”