On Some Positive Linear Operators Preserving the B^{-1}-Convexity of Functions

Yıl 2024, Cilt: 5 Sayı: 2, 134 - 142, 31.07.2024

Mustafa Uzun , Tuncay Tunç

https://doi.org/10.54974/fcmathsci.1393349

Öz

In the study, we first give an inequality that non-negative differentiable functions must satisfy to be B^{-1}-convex. Then, using the inequality, we show that the B^{-1}-convexity property of functions is preserved by Bernstein-Stancu operators, Sz'asz-Mirakjan operators and Baskakov operators. In addition, we compare the concepts B^{-1}-convexity and B-concavity of functions.

Anahtar Kelimeler

B−1 -convexity, Bernstein-Stancu operators, Sz´asz-Mirakjan operators, Baskakov operators, Shape preserving approximation.

Kaynakça

• Adilov G., Yeşilce İ., B^{−1} -convex sets and B^{−1} -measurable maps, Numerical Functional Analysis and Optimization, 33(2), 131-141, 2012.
• Baskakov V.A., An instance of a sequence of linear positive operators in the space of continuous functions, Doklady Akademii Nauk SSSR, 113(2), 249-251, 1957.
• Briec W., Horvath C.D., B-convexity, Optimization, 53(2), 103-127, 2004.
• Briec W., Liang Q.B., On some semilattice structures for production technologies, European Journal of Operational Research, 215(3), 740-749, 2011.
• Briec W., Yeşilce İ., Ky-Fan inequality, Nash equilibria in some idempotent and harmonic convex structure, Journal of Mathematical Analysis and Applications, 508(1), 1-25, 2022.
• Gal S.G., Shape-Preserving Approximation by Real and Complex Polynomials, Birkhauser-Boston, 2008.
• Kemali S., Yeşilce İ., Adilov G., B-convexity, B^{−1} -convexity and their comparison, Numerical Functional Analysis and Optimization, 36(2), 133-146, 2015.
• Meleşteu A.D., About the B-concavity of functions with many variables, Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 31(1), 199-206, 2023.
• Stancu D.D., Asupra unei generilazari a polinoamelor lui Bernstein, Studia Universitatis Babes- Bolyai, 12(2), 31-45, 1969.
• Szász O., Generalization of S. Bernstein’s polynomials to the infinite interval, Journal of Research of the National Bureau of Standards, 45(3), 239-245, 1950.
• Tunç T., Uzun M., On the preservation of B-convexity and B-concavity of functions by Bernstein Operators, Journal of Contemporary Applied Mathematics, 10(2), 77-83, 2020.
• Uzun M., Tunç T., B-convexity and B-concavity preserving property of two-dimensional Bernstein operators, 7th Ifs and Contemporary Mathematics Conference, Türkiye, 1-7, 25-29 May 2021.
• Yeşilce İ., Adilov G., Hermite-Hadamard inequalities for B-convex and B^{−1} -convex functions, International Journal of Nonlinear Analysis and Applications, 8(2), 225-233, 2017.