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    Radon's and Helly's theorems for B-1-Convex sets
    (University of Nis, 2021) Kemali, Serap; Yeşilce, İlknur; Adilov, Gabil
    Helly's, Radon's, and Caratheodory's theorems are the basic theorems of convex analysis and have an important place. These theorems have been studied by different authors for different classes of convexity. Caratheodory's theorem for B-1-convex sets has been proved before by Adilov and Yes , ilce. In this article, Helly's and Radon's theorems are discussed and examined for these sets.
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    Some integral inequalities for the product of s-convex functions in the fourth sense
    (Semnan University, 2022) Kemali, Serap; Sezer Evcan, Sinem; Yeşilce Işık, İlknur; Adilov, Gabil
    n this paper, several novel inequalities are examined for the product of two s-convex functions in the fourth sense. Also, some applications regarding special means and digamma functions are presented.
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    The sharper version for generalized power mean inequalities with negative exponent
    (Element D.O.O., 2023) Tinaztepe, Ramazan; Tinaztepe, Gültekin; Eken, Zeynep; Sezer, Sevda; Kemali, Serap; Yeşilce Işık, İlknur; Sezer Evcan, Sinem
    In this study, the generalized power mean inequalities with a negative parameter are refined using an optimality theorem on the generator function. The optimality theorem requires the study of different cases for the exponents and yields a refinement of the inequality in a neighbourhood of the vectors for which the equality occurs. Then, these local inequalities are generalized to all positive vectors by an appropriate selection of parameters. Also, some of the results are exemplified by numerical calculations.