2024 04 v.39;No.123 24-32
预不变凸函数的q-Hermite-Hadamard型不等式和广义的q-Iyengar型不等式
基金项目(Foundation):
广东省基础与应用基础研究基金项目（2021A1515010055）;;
广东省重点建设学科科研能力提升项目（2021ZDJS055）;;
广东省普通高校科研重点平台和项目—重点领域专项（2023ZDZX4042）;;
广州市海珠区科技计划项目（海科工商信计2022-37）
邮箱(Email):
DOI:
中文作者单位:
海军指挥学院;广东第二师范学院学报编辑部;广东第二师范学院数学学院;
摘要(Abstract):
研究量子积分的Hermite-Hadamard型不等式和Iyengar型不等式，首先建立带有一个参数的量子积分恒等式，然后用引入参数求最值的方法，建立了量子积分的广义的Iyengar型不等式；在一阶量子导数的绝对值是预不变凸函数的情形下，建立了量子积分的Hermite-Hadamard型不等式.
关键词(KeyWords):
Iyengar型不等式;;Hermite-Hadamard型不等式;;量子积分;;预不变凸函数
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参考文献
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[23] GAUCHMAN H. Integral inequalities in q-calculus[J]. Computers and Mathematics with Applications,2004,47(2/3):281-300.
[24] ZUO X, BUTT S I, UMAR M, et al. Novel q-differentiable inequalities[J]. Symmetry, 2023, 15(8):1576.
[25] NOOR M A,NOOR K I,AWAN M U. Some quantum integral inequalities via preinvex functions[J].Applied Mathematics and Computation,2015,269:242-251.
[2] WEIR T,MOND B. Pre-invex functions in multiple objective optimization[J]. Journal of Mathematical Analysis and Applications,1988,136(1):29-38.
[3] MOHAN S R,NEOGY S K. On invex sets and preinvex functions[J]. Journal of Mathematical Analysis and Applications,1995,189(3):901-908.
[4] CRAVEN B D. Invex functions and constrained local minima[J]. Bulletin of the Australian Mathematical Society,1981,24(3):357-366.
[5] YANG X M. A note on preinvexity[J]. Journal of Industrial and Management Optimization,2014,10(4):1319-1321.
[6] NOOR M A. Hermite-Hadamard integral inequalities for log-preinvex functions[J]. J Math Anal Approx Theory,2007,2:126-131.
[7]李觉友.关于s-预不变凸函数的Hadamard型不等式[J].重庆师范大学学报（自然科学版），2010,27(4):5-8.
[8]王海英，符祖峰，李婧，等.多元α-预不变凸函数的Hermite-Hadamard型积分不等式[J].湖北民族大学学报（自然科学版），2023,41(2):246-251.
[9]孙文兵，郑灵红.预不变凸函数的Hermite-Hadamard型分数阶积分不等式的推广[J].中山大学学报（自然科学版），2020,59(4):149-157.
[10]孙文兵.分形空间中的广义预不变凸函数与相关的Hermite-Hadamard型积分不等式[J].浙江大学学报（理学版），2019,46(5):543-549.
[11]时统业，李鼎，朱璟.关于预不变凸函数的Hermite-Hadamard型不等式的一个注记[J].高等数学研究，2017,20(1):23-27.
[12]王海英，符祖峰，高景利，等. E-预不变凸函数的Hermite-Hadamard型积分不等式及应用[J].南阳师范学院学报，2023,22(6):22-28.
[13] TARIBOON J,NTOUYAS S K. Quantum calculus on finite intervals and applications to impulsive difference equations[J]. Advances in Difference Equations,2013,282:1-19.
[14] TARIBOON J,NTOUYAS S K. Quantum integral inequalities on finite intervals[J]. Journal of Inequalities and Applications,2014,121:1-13.
[15] BERMUDO S,KóRUS P,NáPOLES VALD魪S J E. On q-Hermite-Hadamard inequalities for general convex functions[J]. Acta Mathematica Hungarica,2020,162(1):364-374.
[16] SITHO S,ALI M A,BUDAK H,et al. Trapezoid and midpoint type inequalities for preinvex functions via quantum calculus[J]. Mathematics,2021,9(14):1666.
[17] VIVAS-CORTEZ M,KASHURI A,LIKO R,et al. Some new q-integral inequalities using generalized quantum montgomery identity via preinvex functions[J]. Symmetry,2020,12(4):15.
[18] KALSOOM H,ALI M A,ABBAS M,et al. Generalized quantum montgomery identity and Ostrowski type inequalities for preinvex functions[J]. TWMS Journal of Pure and Applied Mathematics,2022,13(1):72-90.
[19] ALI M A,BUDAK H,SARIKAYA M Z,et al. Quantum Ostrowski type inequalities for pre-invex functions[J]. Mathematica Slovaca,2022,72(6):1489-1500.
[20] ALI M A,ABBAS M,BUDAK H,et al. New quantum boundaries for quantum Simpson’s and quantum Newton’s type inequalities for preinvex functions[J]. Advances in Difference Equations,2021,2021:1-21.
[21] IYENGAR K S K. Note on an inequality[J]. The Mathematics Student,1938,6(1):75-76.
[22]时统业. q可微函数和qb可微函数的Iyengar型不等式[J].五邑大学学报（自然科学版），2023,37(1):15-23.
[23] GAUCHMAN H. Integral inequalities in q-calculus[J]. Computers and Mathematics with Applications,2004,47(2/3):281-300.
[24] ZUO X, BUTT S I, UMAR M, et al. Novel q-differentiable inequalities[J]. Symmetry, 2023, 15(8):1576.
[25] NOOR M A,NOOR K I,AWAN M U. Some quantum integral inequalities via preinvex functions[J].Applied Mathematics and Computation,2015,269:242-251.
基本信息:
DOI：
中图分类号:O174.13
引用信息:
[1]时统业,曾志红,曹俊飞.预不变凸函数的q-Hermite-Hadamard型不等式和广义的q-Iyengar型不等式[J].汕头大学学报(自然科学版),2024,39(04):24-32.
基金信息:
广东省基础与应用基础研究基金项目（2021A1515010055）;; 广东省重点建设学科科研能力提升项目（2021ZDJS055）;; 广东省普通高校科研重点平台和项目—重点领域专项（2023ZDZX4042）;; 广州市海珠区科技计划项目（海科工商信计2022-37）
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