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The Hitchhiker’s Guide to the Galaxy is a comedy science fiction novel written by the British novelist Douglas Adams. Even though the story started merely as a radio series, it has grown to be one of the most popular works of science fiction. The genre it belongs to has been defined by Hugo Gernsback, who defined the rules for writing science fiction novels. However, these rules could also be guidelines for the translators to follow in order to produce worthy translations. This paper deals with issues characteristic for the translation of the science fiction genre. Some of those issues are: the translation of newly made-up words and languages, finding the balance between education and entertainment, tone used by the author in order to emphasise the social critique, and re-creating the registers used by alien characters. Vodič kroz galaksiju za autostopere roman je humoristične znanstvene fantastike britanskog autora Douglasa Adamsa. Iako je priča ovog romana započela tek kao radijska emisija, danas je ovo jedno od najpopularnijih djela znanstvene fantastike. Žanr kojem pripada odredio je Hugo Gernsback, koji je definirao pravila pisanja znanstveno fantastičnog romana. Međutim, ova pravila također mogu pomoći prevoditeljima kako bi stvorili vjerodostojne prijevode. Ovaj rad bavi se problemima karakterističnim za prevođenje žanra znanstvene fantastike. Neki od tih problema su: predvođenje novih riječi i jezika, pronalaženje ravnoteže između edukacije i zabave, ton kojeg koristi autor kako bi naglasio društvenu kritiku, te imitiranje registara koje koriste likovi izvanzemaljaca.

This talk deals with Opial inequality and its famous generalizations, extensions and refinements, i.e. with Opial-type inequalities. The Opial inequality has been generalized and extended in several directions. We obtain general Opial-type inequalities for measurable functions and for the quotient of functions. Application to numerous symmetric functions gives results that involve Green’s functions, Lidstone’s series and Hermite’s interpolating polynomials.

U disertaciji je promatrana Opialova nejednakost i njezina poopćenja i profinjenja, kratko rečeno, proučavane su nejednakosti Opialova tipa. Prvo su dobivene nove nejednakosti Opialova tipa za konveksne funkcije koje su poopćenja i profinjenja Opialove, Wilettove, Godunova-Levinove i Rozanovine nejednakosti. Potom su dokazani rezultati i za više varijabli. Također su dobivene nove nejednakosti Opialova tipa za konveksne i relativno konveksne funkcije usko povezane s Mitrinović-Pečarićevim rezultatima, primjenom kojih slijede nejednakosti za razlomljene derivacije Riemann-Liouvilleovog, Canavatijevog i Caputovog tipa, te za Riemann-Liouville razlomljene integrale. Dokazani su teoremi srednje vrijednosti za funkcionale pridružene novodobivenim nejednakostima. Dano je nekoliko familija funkcija koje omogućavaju konstrukcije familije eksponencijalno konveksnih funkcija, te sredine Stolarskyjevog tipa koje imaju svojstvo monotonosti. Nadalje, razmatrana je opća nejednakost Opialova tipa za izmjerive funkcije te potom za kvocijent funkcija. Primjenom na razne simetrične funkcije dobiveni su novi rezultati vezani za Greenove funkcije, Lidstoneove redove i Hermiteove interpolacijske polinome. This thesis deals with Opial inequality and its famous generalizations, extensions and refinements, i.e. with Opial-type inequalities. First, new Opial-type inequalities for convex functions are presented, some of which are generalization and some are refinement of Opial’s, Willett’s, Godunova-Levin’s and Rozanova’s inequality. Then results for more variables are proven. Moreover, new Opial-type inequalites are obtained for convex and relatively convex functions closelly connected to Mitrinović-Pečarić’s results, and application of these results yields inequalities for fractional derivatives of the Riemann-Liouville, Canavati and Caputo type and for the Riemann-Liouville fractional integrals. Mean value results are proven for linear functionals constructed from the newly obtained inequalities. Several examples of families of functions are given which enable construction of families of exponentially convex function and monotonic Stolarsky-type means. Further, general Opial-type inequalities for measurable functions and for the quotient of functions are obtained. Application to numerous symmetric functions gives results that involve Green’s functions, Lidstone’s series and Hermite’s interpolating polynomials.

The purpose of this corrigendum is to correct an error in the earlier paper by the authors: Generalizations of Opial-type inequalities in several independent variables, Demonstratio Math.

In this paper we obtain new refinements of Jessen's functional, defined by means of positive linear functionals. Derived results are then applied to weighted generalized and power means. We also obtain new refinements of numerous classical inequalities such as arithmetic-geometric mean inequality, Young's inequality and Holder's inequality.

In this paper we consider generalizations of Opial's inequality due to Willett, Godunova, Levin and Rozanova. Cauchy type mean value theorems are proved and used in studying Stolarsky type means defined by the obtained inequalities. Also, a method of producing n-exponentially convex and exponentially convex functions is applied.

In this paper we give extensions of Opial-type integral inequalities and use them to obtain a generalization of an inequality due to Agarwal and Pang. Applications with respect to fractional derivatives and fractional integrals are also given.

In this paper we consider a certain class of convex functions in Opial-type integral inequalities. Cauchy type mean value theorems are proved and used in studying Stolarsky type means defined by the observed integral inequalities. A method of producing n- exponentially convex and exponentially convex functions is applied. Also, some new Opial-type equalities are given involving fractional integrals and fractional derivatives.

In this talk we give a general Opial type inequality. Our result contains two functions, convex and concave function. We prove a new general inequality on a measure space. The obtained inequalities are not direct generalizations of the Opial inequality but they are of Opial type because integrals contain function and its integral representation. We apply our result to numerous symmetric functions and obtain new results that involve Green's functions, Lidstone series and the Hermite interpolating polynomials.

We consider generalizations of Opial's inequality due to Willet, Godunova, Levin and Rozanova in one variable and obtain certain improvements. Then we extend Willet's and Rozanova's Opial-type inequalities to inequalities in several independent variables. Also, we present some new Opial-type inequalities in several independent variables.

We present extensions of Opial-type inequalities and use them to obtain a generalization of an inequality due to Mitrinović and Pečarić for relatively convex functions. Also, some new Opial-type inequalities are given involving different types of fractional integrals and fractional derivatives as applications.