Generalizations of the steffensen integral inequality for pseudo-integrals
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Jing Guo
Abstract
In this paper, our aim is to prove certain kinds of Steffensen type integral inequalities for the pseudo-integral and the discrete pseudo-integral. The observations concern two cases of the real semiring with pseudo-operations with respect to pseudo-integrals: the first semiring, where pseudo-operations are defined via a monotone and continuous function g, the second semiring, when pseudo-operations are given by an idempotent addition and a generated pseudo-multiplication. Moreover, the discrete pseudo-integral is based on symmetric pseudo-addition and pseudo-multiplication, where the generator g is odd and increasing. In each case, several practical examples are presented to illustrate these results.
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((Communicated by Anatolij Dvurečenskij))
References
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Articles in the same Issue
- Regular Papers
- Generalized hyperharmonic number sums with reciprocal binomial coefficients
- Gini index on generalized r-partitions
- Multiplicative functions of special type on Piatetski-Shapiro sequences
- Strengthenings of Young-type inequalities and the arithmetic geometric mean inequality
- Generalizations of the steffensen integral inequality for pseudo-integrals
- Subordination-implication problems concerning the nephroid starlikeness of analytic functions
- Boundedness and almost periodicity of solutions of linear differential systems
- On variational approaches for fractional differential equations
- Approximity of asymmetric metric spaces
- Approximation theorems for the new construction of Balázs operators and its applications
- On η-biharmonic hypersurfaces in pseudo-Riemannian space forms
- Chen’s first inequality for hemi-slant warped products in nearly trans-Sasakian manifolds
- Induced mappings on symmetric products of Hausdorff spaces
- The Teissier-G family of distributions: Properties and applications
- A new extension of the beta generator of distributions
- A new family of compound exponentiated logarithmic distributions with applications to lifetime data
- On two correlated linear models with common and different parameters
- On some applications of Duhamel operators
