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Öğe A refinement of the Bergstrom inequality(TUBITAK, 2021) Tinaztepe, Gültekin; Yeşilce, İlknur; Adilov, GabilIn this paper, the Bergstrom inequality is studied, and a refinement of this inequality is obtained by performing the optimality conditions based on abstract concavity. Some numerical experiments are given to illustrate the efficacy of the refinement.Öğe Hermite-hadamard type inequalities for B-1-convex functions involving generalized fractional integral operators(Univ Nis, Fac Sci Math, 2018) Yeşilce, İlknur; Adilov, GabilB-1-convexity is an abstract convexity type. We obtained Hermite-Hadamard inequality for B-1-convex functions. But now, there are new and more general integral operator types that are fractional integrals. Thus, we need to prove Hermite-Hadamard inequalities involving different fractional integral operator types with this article.Öğe Inequalities involving general fractional integrals of p-convex functions(TUBITAK, 2023) Işık, İlknur Yeşilce; Tinaztepe, Gültekin; Kemal, Serap; Adilov, GabilThe Hermite-Hadamard type inequalities involving fractional integral operations for p-convex functions with respect to another function are studied. Then, the inequalities via Riemann-Liouville and Hadamard fractional integrals are presented specially. Using the obtained results, some inequality relations among special functions including beta and incomplete beta functions, gamma and incomplete gamma functions, and hypergeometric functions are presented.Öğe Radon's and Helly's theorems for B-1-Convex sets(University of Nis, 2021) Kemali, Serap; Yeşilce, İlknur; Adilov, GabilHelly'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.Öğe 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, Gabiln 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.