References
- I. Bárány, A generalization of Carathéodory's theorem, Discrete Math. 40 (1982), no. 2–3, 141–152.
- A. Barvinok, A Course in Convexity, Grad. Stud. Math., 54, American Mathematical Society, Providence, RI, 2002.
- C. Carathéodory, Über den Variabilitätsbereich der Fourier'schen Konstanten von positiven harmonischen Funktionen, Rend. Circ. Mat. Palermo (1884–1940) 32 (1911), no. 1, 193–217.
- P. Erdös and G. Szekeres, A combinatorial problem in geometry, Compositio Math. 2 (1935), 463–470.
- M. Essén, A theorem on convex sequences, Analysis 2 (1982), no. 1–4, 231–252.
- S. Gaubert, P. Butkovič, and R. Cuninghame-Green, Minimal (max, +) realization of convex sequences, SIAM J. Control Optim. 36 (1998), no. 1, 137–147.
- E. Helly, Über Mengen konvexer Körper mit gemeinschaftlichen Punkte, Jber. Deutsch. Math.-Verein. 32 (1923), 175–176.
- J. Jiménez-Garrido, J. Sanz, and G. Schindl, Log-convex sequences and nonzero proximate orders, J. Math. Anal. Appl. 448 (2017), no. 2, 1572–1599.
- X.Z. Krasniqi, On α-convex sequences of higher order, J. Numer. Anal. Approx. Theory 45 (2016), no. 2, 177–182.
- M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities, Polish Scientific Editors and Silesian University, Warszawa-Kraków-Katowice, 1985.
- Z. Latreuch and B. Belaïdi, New inequalities for convex sequences with applications, Int. J. Open Probl. Comput. Sci. Math. 5 (2012), no. 3, 15–27.
- A.McD. Mercer, Polynomials and convex sequence inequalities, JIPAM. J. Inequal. Pure Appl. Math. 6 (2005), no. 1, Article 8, 4 pp.
- I.Ž. Milovanović and E.I. Milovanović, Some properties of Lk-convex sequences, Bull. Int. Math. Virtual Inst. 5 (2015), no. 1, 33–36.
- D.S. Mitrinović, Analytic Inequalities (in cooperation with P.M. Vasić), Die Grundlehren der mathematischen Wissenschaften, Band 165, Springer-Verlag, New York-Berlin, 1970.
- G.M. Molnár and Z. Páles, On convex and concave sequences and their applications, Math. Inequal. Appl. 25 (2022), no. 3, 727–750.
- J.E. Pečarić, On some inequalities for convex sequences, Publ. Inst. Math. (Beograd) (N.S.) 33(47) (1983), 173–178.
- A. Pinkus and D. Wulbert, Extending n-convex functions, Studia Math. 171 (2005), no. 2, 125–152.
- J. Radon, Mengen konvexer Körper, die einen gemeinsamen Punkt enthalten, Math. Ann. 83 (1921), no. 1–2, 113–115.
- D.F. Sofonea, I. Ţincu, and A.M. Acu, Convex sequences of higher order, Filomat 32 (2018), no. 13, 4655–4663.
- E. Steinitz, Bedingt konvergente Reihen und konvexe Systeme, J. Reine Angew. Math. 143 (1913), 128–176.
- S. Wu and L. Debnath, Inequalities for convex sequences and their applications, Comput. Math. Appl. 54 (2007), no. 4, 525–534.
Language: English
Page range: 219 - 229
Submitted on: Jan 18, 2025
Accepted on: Oct 9, 2025
Published on: Nov 2, 2025
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© 2025 Angshuman R. Goswami, István Szalkai, published by University of Silesia in Katowice, Institute of Mathematics
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