7 research outputs found
On the Minkowski-H\"{o}lder type inequalities for generalized Sugeno integrals with an application
In this paper, we use a new method to obtain the necessary and sufficient
condition guaranteeing the validity of the Minkowski-H\"{o}lder type inequality
for the generalized upper Sugeno integral in the case of functions belonging to
a wider class than the comonotone functions. As a by-product, we show that the
Minkowski type inequality for seminormed fuzzy integral presented by Daraby and
Ghadimi in General Minkowski type and related inequalities for seminormed fuzzy
integrals, Sahand Communications in Mathematical Analysis 1 (2014) 9--20 is not
true. Next, we study the Minkowski-H\"{o}lder inequality for the lower Sugeno
integral and the class of -subadditive functions introduced in On
Chebyshev type inequalities for generalized Sugeno integrals, Fuzzy Sets and
Systems 244 (2014) 51--62. The results are applied to derive new metrics on the
space of measurable functions in the setting of nonadditive measure theory. We
also give a partial answer to the open problem 2.22 posed by
Borzov\'a-Moln\'arov\'a and et al in The smallest semicopula-based universal
integrals I: Properties and characterizations, Fuzzy Sets and Systems 271
(2015) 1--17.Comment: 19 page
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
Advances in Optimization and Nonlinear Analysis
The present book focuses on that part of calculus of variations, optimization, nonlinear analysis and related applications which combines tools and methods from partial differential equations with geometrical techniques. More precisely, this work is devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of solving a wide range of problems. The book is a valuable guide for researchers, engineers and students in the field of mathematics, operations research, optimal control science, artificial intelligence, management science and economics