Papers by Ludmila Nikolova
Journal of Inequalities and Applications, Feb 21, 2023
Annals of Functional Analysis, 2011
Continuous form of the Gauss-Polya inequality
Journal of Inequalities and Applications, Jan 12, 2012
Complex interpolation for family of Banach spaces
Ukrainian Mathematical Journal, 1982
Aktualʹnye napravleniâ naučnyh issledovanij XXI veka: teoriâ i praktika, 2017
Mathematical Inequalities & Applications, 2016
We give a generalization of the Chebyshev-Grüss inequality by using the concept of derivative on ... more We give a generalization of the Chebyshev-Grüss inequality by using the concept of derivative on time scales combined with application of the Chebyshev inequality involving two linear isotonic functionals. This approach covers integral case, discrete case, results from fractional and quantum calculus.
Geometric constants for Banach spaces with absolute normalized norms which corresponding functions are comparable
Journal of Nonlinear and Convex Analysis, 2013
In this paper we consider some geometric constants of ${; ; ; \bf C}; ; ; ^2$ equipped with an ab... more In this paper we consider some geometric constants of ${; ; ; \bf C}; ; ; ^2$ equipped with an absolute normalized norm such as: the James constant $J(\|.\|_{; ; ; \psi}; ; ; )$, the von Neumann- -Jordan constant $C_{; ; ; NJ}; ; ; (\|.\|_{; ; ; \psi}; ; ; )$, the Gao constants $E(\|.\|_{; ; ; \psi}; ; ; )$ and $f(\|.\|_{; ; ; \psi}; ; ; )$, the Zb\u{; ; ; a}; ; ; ganu constant $C_{; ; ; Z}; ; ; (\|.\|_{; ; ; \psi}; ; ; )$ and constant $A_2(\|.\|_{; ; ; \psi}; ; ; )$. In particular we investigate relations involving these constants of the norms $\|.\|_{; ; ; \psi}; ; ; $ and $\|.\|_{; ; ; \psi_*}; ; ; $ where the convex functions $\psi$ and $ \psi_*$ are comparable. Also, we determine these constants when norm is a mean of two norms. Finally, these constants are calculated for some spaces such as the $X^p$ space, the Ces\`{; ; ; a}; ; ; ro sequence space etc.
Norms of interpolation operators controlled by the Dicesar function
Journal of Mathematical Inequalities, 2015
We consider the so-called DEC inequality via theory of isotonic linear functionals. The DEC inequ... more We consider the so-called DEC inequality via theory of isotonic linear functionals. The DEC inequality is a refinement of the well-known Cauchy inequality and its well-known particular cases are the Milne and the Callebaut inequalities. We also investigate properties of some functionals which are arised from the DEC inequality.
Archiv der Mathematik, 1996
Lions–Peetre reiteration formulas for triples and their applications
Studia Mathematica, 2001
Journal of Inequalities and Applications
Some new refined versions of the Jensen, Minkowski, and Hardy inequalities are stated and proved.... more Some new refined versions of the Jensen, Minkowski, and Hardy inequalities are stated and proved. In particular, these results both generalize and unify several results of this type. Some results are also new for the classical situation.
Journal of Inequalities and Applications
In this paper we prove new continuous refinements of some Jensen type inequalities in both direct... more In this paper we prove new continuous refinements of some Jensen type inequalities in both direct and reversed forms. As applications we also derive some continuous refinements of Hermite–Hadamard, Hölder, and Popoviciu type inequalities. As particular cases we point out the corresponding results for sums and integrals showing that our results contain both several well-known but also some new results for these special cases.
Miskolc Mathematical Notes, 2017
In the paper we prove several inequalities involving two isotonic linear functionals. We consider... more In the paper we prove several inequalities involving two isotonic linear functionals. We consider inequalities for functions with variable bounds, for Lipschitz and Hölder type functions etc. These results give us an elegant method for obtaining a number of inequalities for various kinds of fractional integral operators such as for the Riemann-Liouville fractional integral operator, the Hadamard fractional integral operator, fractional hyperqeometric integral and corresponding q-integrals.
We consider mappings generated by inequalities for isotonic linear functionals such as the inequa... more We consider mappings generated by inequalities for isotonic linear functionals such as the inequalities of Chebyshev, Beckenbach-Dresher, Jensen-Mercer, Jensen, Hölder, Minkowski and their reversed versions. Properties like quasilinearity, boundedness and monotonicity are proved. Also, properties of the composite functional x 7→ h(v(x))Φ g(x) v(x) are mentioned, where g and v are functions associated with the mappings generated by the inequalities and Φ is a h-concave monotone function.
Mathematical Inequalities & Applications, 2021
Some new inequalities of Hardy-type in Banach function space settings are proved and discussed. I... more Some new inequalities of Hardy-type in Banach function space settings are proved and discussed. In particular, these results generalize and unify several classical Hardy-type inequalities. Some results are new also in the classical situation.
Mathematische Nachrichten, 2019
In this paper we derive some new inequalities involving the Hardy operator, using some estimates ... more In this paper we derive some new inequalities involving the Hardy operator, using some estimates of the Jensen functional, continuous form generalization of the Bellman inequality and a Banach space variant of it. Some results are generalized to the case of Banach lattices on (0, ], 0 < ≤ ∞.
Mathematical Inequalities & Applications, 2019
The main aim of this paper is to give a continuous form of the Gauss-Pólya type inequalities i.e.... more The main aim of this paper is to give a continuous form of the Gauss-Pólya type inequalities i.e. to give inequalities involving infinitely many functions. We consider inequalities which involve derivatives and which structure is related to the Hölder inequality. Also, some properties of the corresponding functionals are given.
Journal of Mathematical Inequalities, 2018
We consider inequalities which involve two linear isotonic functionals. We give two variants of t... more We consider inequalities which involve two linear isotonic functionals. We give two variants of the Cauchy inequality and few Pólya-Szegö type inequalities in which functions with variable bounds occurred. With help of these inequalities we are able to obtain a new bound for the Chebyshev difference and give some particular cases. Connections of the presented results with earlier results involving fractional integrals are also pointed out. Mathematics subject classification (2010): 26D15.
Uploads
Papers by Ludmila Nikolova