Converse Edmundson-Lah-Ribarič inequalities and related results

Definirat će se nova klasa funkcija koja proširuje klasu 3-konveksnih funkcija za koju će se dokazati generalizacija Levinsonovog tipa Edmundson-Lah-Ribaričeve nejednakosti. Dokazat će se da analogne generalizacije vrijede i za Edmundson-Lah-Ribaričevu nejednakost za hermitske operatore u Hilbertovom prostoru, te za skalarni produkt istih. Dalje, promatrat će se Jensenova i Edmundson-Lah-Ribaričeva nejednakost za linearne funkcionale. Dobit će se njihovi obrati u obliku razlike, kao i profinjenja i poboljšanja spomenutih obrata. Dobiveni rezultati primijenit će se na generalizirane sredine i na neke poznate nejednakosti (Hölderovu, Hermite-Hadamardovu, Giaccardijevu i Petrovićevu nejednakost). Dobit će se i obrati Jensenove i Edmundson-Lah-Ribaričeve operatorske nejednakosti, kao i daljnja profinjenja i poboljšanja istih. Dobiveni opći rezultati primijenit će se na kvazi-aritmetičke operatorske sredine, te na potencijalne operatorske sredine. Također će se dobiti i obrati Andove i Davis-Choijeve nejednakosti za pozitivna linearna preslikavanja, te Edmundson-Lah-Ribaričeva nejednakost i njen obrat u obliku razlike za pozitivna linearna preslikavanja. Dokazat će se i obrati u obliku razlike i kvocijenta za poseban tip poopćenih koneksija - solidarities koji uključuje i koneksije, te za relativnu operatorsku entropiju.A new class of functions that extends the class of 3-convex functions will be defined, and Levinson’s type generalization of the Edmundson-Lah-Ribarič inequality will be proved for those functions. Analogue generalizations of the Edmundson-Lah-Ribarič inequality for self-adjoint operators in Hilbert space and for their scalar product will be proved. Next, inequalities of Jensen and Edmundson-Lah-Ribarič for positive linear functionals will be studied. New inequalities of difference type, as well as their refinements and improvements, will be obtained. These results will be applied to generalized means and some famous inequalities (the ones of Hölder, Hermite-Hadamard, Giaccardi and Petrović). Further, converses of the Jensen and Edmundson-Lah-Ribarič operator inequalities and their refinements and improvements will be obtained. General results will be applied to quasi-arithmetic operator means and to potential operator means. Finally, converses of Ando’s and Davis-Choi’s inequality, as well as the Edmundson-Lah-Ribarič and its converse of difference type for positive unital mappings, will be studied. Ratio and difference type converses will be proved for a special type of solidarities which includes connections, and for relative operator entropy

Converse Edmundson-Lah-Ribarič inequalities and related results

Definirat će se nova klasa funkcija koja proširuje klasu 3-konveksnih funkcija za koju će se dokazati generalizacija Levinsonovog tipa Edmundson-Lah-Ribaričeve nejednakosti. Dokazat će se da analogne generalizacije vrijede i za Edmundson-Lah-Ribaričevu nejednakost za hermitske operatore u Hilbertovom prostoru, te za skalarni produkt istih. Dalje, promatrat će se Jensenova i Edmundson-Lah-Ribaričeva nejednakost za linearne funkcionale. Dobit će se njihovi obrati u obliku razlike, kao i profinjenja i poboljšanja spomenutih obrata. Dobiveni rezultati primijenit će se na generalizirane sredine i na neke poznate nejednakosti (Hölderovu, Hermite-Hadamardovu, Giaccardijevu i Petrovićevu nejednakost). Dobit će se i obrati Jensenove i Edmundson-Lah-Ribaričeve operatorske nejednakosti, kao i daljnja profinjenja i poboljšanja istih. Dobiveni opći rezultati primijenit će se na kvazi-aritmetičke operatorske sredine, te na potencijalne operatorske sredine. Također će se dobiti i obrati Andove i Davis-Choijeve nejednakosti za pozitivna linearna preslikavanja, te Edmundson-Lah-Ribaričeva nejednakost i njen obrat u obliku razlike za pozitivna linearna preslikavanja. Dokazat će se i obrati u obliku razlike i kvocijenta za poseban tip poopćenih koneksija - solidarities koji uključuje i koneksije, te za relativnu operatorsku entropiju.A new class of functions that extends the class of 3-convex functions will be defined, and Levinson’s type generalization of the Edmundson-Lah-Ribarič inequality will be proved for those functions. Analogue generalizations of the Edmundson-Lah-Ribarič inequality for self-adjoint operators in Hilbert space and for their scalar product will be proved. Next, inequalities of Jensen and Edmundson-Lah-Ribarič for positive linear functionals will be studied. New inequalities of difference type, as well as their refinements and improvements, will be obtained. These results will be applied to generalized means and some famous inequalities (the ones of Hölder, Hermite-Hadamard, Giaccardi and Petrović). Further, converses of the Jensen and Edmundson-Lah-Ribarič operator inequalities and their refinements and improvements will be obtained. General results will be applied to quasi-arithmetic operator means and to potential operator means. Finally, converses of Ando’s and Davis-Choi’s inequality, as well as the Edmundson-Lah-Ribarič and its converse of difference type for positive unital mappings, will be studied. Ratio and difference type converses will be proved for a special type of solidarities which includes connections, and for relative operator entropy

Converse Edmundson-Lah-Ribarič inequalities and related results

Definirat će se nova klasa funkcija koja proširuje klasu 3-konveksnih funkcija za koju će se dokazati generalizacija Levinsonovog tipa Edmundson-Lah-Ribaričeve nejednakosti. Dokazat će se da analogne generalizacije vrijede i za Edmundson-Lah-Ribaričevu nejednakost za hermitske operatore u Hilbertovom prostoru, te za skalarni produkt istih. Dalje, promatrat će se Jensenova i Edmundson-Lah-Ribaričeva nejednakost za linearne funkcionale. Dobit će se njihovi obrati u obliku razlike, kao i profinjenja i poboljšanja spomenutih obrata. Dobiveni rezultati primijenit će se na generalizirane sredine i na neke poznate nejednakosti (Hölderovu, Hermite-Hadamardovu, Giaccardijevu i Petrovićevu nejednakost). Dobit će se i obrati Jensenove i Edmundson-Lah-Ribaričeve operatorske nejednakosti, kao i daljnja profinjenja i poboljšanja istih. Dobiveni opći rezultati primijenit će se na kvazi-aritmetičke operatorske sredine, te na potencijalne operatorske sredine. Također će se dobiti i obrati Andove i Davis-Choijeve nejednakosti za pozitivna linearna preslikavanja, te Edmundson-Lah-Ribaričeva nejednakost i njen obrat u obliku razlike za pozitivna linearna preslikavanja. Dokazat će se i obrati u obliku razlike i kvocijenta za poseban tip poopćenih koneksija - solidarities koji uključuje i koneksije, te za relativnu operatorsku entropiju.A new class of functions that extends the class of 3-convex functions will be defined, and Levinson’s type generalization of the Edmundson-Lah-Ribarič inequality will be proved for those functions. Analogue generalizations of the Edmundson-Lah-Ribarič inequality for self-adjoint operators in Hilbert space and for their scalar product will be proved. Next, inequalities of Jensen and Edmundson-Lah-Ribarič for positive linear functionals will be studied. New inequalities of difference type, as well as their refinements and improvements, will be obtained. These results will be applied to generalized means and some famous inequalities (the ones of Hölder, Hermite-Hadamard, Giaccardi and Petrović). Further, converses of the Jensen and Edmundson-Lah-Ribarič operator inequalities and their refinements and improvements will be obtained. General results will be applied to quasi-arithmetic operator means and to potential operator means. Finally, converses of Ando’s and Davis-Choi’s inequality, as well as the Edmundson-Lah-Ribarič and its converse of difference type for positive unital mappings, will be studied. Ratio and difference type converses will be proved for a special type of solidarities which includes connections, and for relative operator entropy

Seminars in Statistics in MS Excel

Ovaj priručnik prikazuje način rješavanja problema statističke analize podataka koji se proučavaju u sklopu kolegija „Statistika“ u svrhu njihove lakše analize pomoću programa MS Excel korištenjem statističkih funkcija ili alata „Analiza podataka“. Obrađuju se osnovni pojmovi deskriptivne statistike (grafički prikazi, mjere centralne tendencije i mjere raspršenosti podataka), i osnove inferencijalne statistike s težištem na linearnoj regresiji i testiranju hipoteza.This manual shows how to solve problems of statistical analysis that are studied as part of the course "Statistics" for the purpose of their easier analysis with the MS Excel software using statistical functions or the "Data Analysis" tool. The basic concepts of descriptive statistics (graphical representations, measures of central tendency and measures of dispersion) and the basics of inferential statistics with a focus on linear regression and hypothesis testing are covered

Seminars in Statistics in MS Excel

Ovaj priručnik prikazuje način rješavanja problema statističke analize podataka koji se proučavaju u sklopu kolegija „Statistika“ u svrhu njihove lakše analize pomoću programa MS Excel korištenjem statističkih funkcija ili alata „Analiza podataka“. Obrađuju se osnovni pojmovi deskriptivne statistike (grafički prikazi, mjere centralne tendencije i mjere raspršenosti podataka), i osnove inferencijalne statistike s težištem na linearnoj regresiji i testiranju hipoteza.This manual shows how to solve problems of statistical analysis that are studied as part of the course "Statistics" for the purpose of their easier analysis with the MS Excel software using statistical functions or the "Data Analysis" tool. The basic concepts of descriptive statistics (graphical representations, measures of central tendency and measures of dispersion) and the basics of inferential statistics with a focus on linear regression and hypothesis testing are covered

Jensen-type inequalities on time scales for n-convex functions

In this paper, the authors establish some lower and upper bounds for the difference in the Edmundson-Lah-Ribarič inequality in time scales calculus that holds for the class of n-convex functions by utilizing some scalar inequalities obtained via Hermite's interpolating polynomial. In addition, the authors also establish different lower and upper bounds for the difference in the Jensen inequality as a byproduct from the results of the Edmundson-Lah-Ribarič inequality. The main results are applied to obtain new converse inequalities for generalized means and power means in the time scale settings

Converses of the Edumundson-Lah-Ribarič inequality for generalized Csiszár divergence with applications to Zipf-Mandelbrot law

Summary: "In this paper we obtain some estimates for the generalized f-divergence functional via converses of the Jensen and Edmundson-Lah-Ribarič inequalities for convex functions, and then we obtain some estimates for the Kullback-Leibler divergence. All of the obtained results are applied to Zipf-Mandelbrot law and Zipf law.