caa a22 4500 605508569 CHVBK 20210128100637.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s00010-013-0252-4 doi (NATIONALLICENCE)springer-10.1007/s00010-013-0252-4 General Opial type inequality [Elektronische Daten] [Ana Barbir, Kristina Himmelreich, Josip Pečarić] In this paper our goal is to give a general Opial type inequality. We consider two functions, convex and concave and prove a new general inequality on a measure space (Ω,Σ,μ). The obtained inequalities are not direct generalizations of the Opial inequality but are of Opial type because the integrals contain a 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's interpolating polynomials. Springer Basel, 2014 Opial inequality nationallicence green function nationallicence jensen inequality nationallicence lidstone polynomial nationallicence hermite interpolating polynomial nationallicence Barbir Ana Faculty of Civil Engineering and Architecture, Matice rvatske 15, 21 000, Split, Croatia aut Himmelreich Kristina Faculty of Textile Technology and University of Zagreb, Prilaz baruna Filipovića 28a, 10000, Zagreb, Croatia aut Pečarić Josip Faculty of Textile Technology and University of Zagreb, Prilaz baruna Filipovića 28a, 10000, Zagreb, Croatia aut Aequationes mathematicae Springer Basel 89/3(2015-06-01), 641-655 0001-9054 89:3<641 2015 89 10 https://doi.org/10.1007/s00010-013-0252-4 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00010-013-0252-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Barbir Ana Faculty of Civil Engineering and Architecture, Matice rvatske 15, 21 000, Split, Croatia aut NATIONALLICENCE 700 1- Himmelreich Kristina Faculty of Textile Technology and University of Zagreb, Prilaz baruna Filipovića 28a, 10000, Zagreb, Croatia aut NATIONALLICENCE 700 1- Pečarić Josip Faculty of Textile Technology and University of Zagreb, Prilaz baruna Filipovića 28a, 10000, Zagreb, Croatia aut NATIONALLICENCE 773 0- Aequationes mathematicae Springer Basel 89/3(2015-06-01), 641-655 0001-9054 89:3<641 2015 89 10