12 results
Search Results
2. Generalized fractional integral inequalities of Hermite–Hadamard type for harmonically convex functions.
- Author
-
Zhao, Dafang, Ali, Muhammad Aamir, Kashuri, Artion, and Budak, Hüseyin
- Subjects
INTEGRAL inequalities ,FRACTIONAL integrals ,GENERALIZED integrals ,CONVEX functions ,MATHEMATICS - Abstract
In this paper, we establish inequalities of Hermite–Hadamard type for harmonically convex functions using a generalized fractional integral. The results of our paper are an extension of previously obtained results (İşcan in Hacet. J. Math. Stat. 43(6):935–942, 2014 and İşcan and Wu in Appl. Math. Comput. 238:237–244, 2014). We also discuss some special cases for our main results and obtain new inequalities of Hermite–Hadamard type. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
3. Weighted Hermite–Hadamard type inclusions for products of co-ordinated convex interval-valued functions.
- Author
-
Kara, Hasan, Budak, Hüseyin, Ali, Muhammad Aamir, Sarikaya, Mehmet Zeki, and Chu, Yu-Ming
- Subjects
CONVEX functions ,GENERALIZATION - Abstract
In this paper, we establish some Hermite–Hadamard–Fejér type inclusions for the product of two co-ordinated convex interval-valued functions. These inclusions are generalizations of some results given in earlier works. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
4. Sharp trapezoid and mid-point type inequalities on closed balls in R3.
- Author
-
Rostamian Delavar, M.
- Subjects
TRAPEZOIDS ,SPHERICAL coordinates ,MATHEMATICAL equivalence - Abstract
This paper deals with some trapezoid and mid-point type inequalities on closed balls in R 3 . Three kinds of functions are considered: convex, Lipschitz, and bounded functions. The spherical coordinates are used to obtain sharp inequalities. Also a reverse result is given for the right-hand side of Hermite–Hadamard's inequality obtained on closed balls in R 3 . [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
5. On fractional Simpson type integral inequalities for co-ordinated convex functions.
- Author
-
Khan, Sundas and Budak, Hüseyin
- Subjects
CONVEX functions ,FRACTIONAL integrals ,INTEGRAL inequalities ,GENERALIZED integrals ,FRACTIONAL calculus ,RECTANGLES - Abstract
In this study, we prove equality for twice partially differentiable mappings involving the double generalized fractional integral. Using the established identity, we offer some Simpson's type inequalities for partially differentiable co-ordinated convex functions in a rectangle from the plane R 2 . [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
6. A Generalization of Archimedes’ Theorem on the Area of a Parabolic Segment
- Author
-
Grigoryan Armen, Ignaciuk Szymon, and Parol Maciej
- Subjects
archimedes’ theorem ,parabolic segment ,multiple integral ,spherical coordinates ,26b15 ,28a75 ,51m25 ,Mathematics ,QA1-939 - Abstract
Archimedes’ well known theorem on the area of a parabolic segment says that this area is 4/3 of the area of a certain inscribed triangle. In this paper we generalize this theorem to the n-dimensional euclidean space, n ≥ 3. It appears that the ratio of the volume of an n-dimensional solid bounded by an (n − 1)-dimensional hyper-paraboloid and an (n − 1)-dimensional hyperplane and the volume of a certain inscribed cone (we analogously repeat Archimedes’ procedure) depends only on the dimension of the euclidean space and it equals to 2n/(n +1).
- Published
- 2021
- Full Text
- View/download PDF
7. On generalized Ostrowski, Simpson and Trapezoidal type inequalities for co-ordinated convex functions via generalized fractional integrals.
- Author
-
Budak, Hüseyin, Hezenci, Fatih, and Kara, Hasan
- Subjects
FRACTIONAL integrals ,GENERALIZED integrals ,CONVEX functions ,RECTANGLES - Abstract
In this study, we prove an identity for twice partially differentiable mappings involving the double generalized fractional integral and some parameters. By using this established identity, we offer some generalized inequalities for differentiable co-ordinated convex functions with a rectangle in the plane R 2 . Furthermore, by special choice of parameters in our main results, we obtain several well-known inequalities such as the Ostrowski inequality, trapezoidal inequality, and the Simpson inequality for Riemann and Riemann–Liouville fractional integrals. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
8. Opial type inequalities for double Riemann-Stieltjes integrals
- Author
-
Budak Hüseyin
- Subjects
opial inequality ,hölder’s inequality ,primary: 26d15 ,26d10 ,26b15 ,Mathematics ,QA1-939 - Abstract
In this paper, we establish some Opial type inequalities for Riemann-Stieltjes integrals of functions with two variables. The obtained inequalities generalize those previously demonstrated (see [2])
- Published
- 2018
- Full Text
- View/download PDF
9. Weighted Hermite-Hadamard type inclusions for products of co-ordinated convex interval-valued functions
- Author
-
Hasan Kara, Hüseyin Budak, Yu-Ming Chu, Mehmet Zeki Sarikaya, Muhammad Ali, and [Belirlenecek]
- Subjects
Pure mathematics ,Algebra and Number Theory ,Partial differential equation ,Hermite polynomials ,Functional analysis ,Applied Mathematics ,lcsh:Mathematics ,Regular polygon ,Mathematics::Classical Analysis and ODEs ,Convex interval-valued functions ,Co-ordinated convex interval-valued functions ,Type (model theory) ,lcsh:QA1-939 ,Hermite-Hadamard inclusions ,26B25 ,26B15 ,26D15 ,Hadamard transform ,Product (mathematics) ,Ordinary differential equation ,Hermite–Hadamard inclusions ,26D07 ,Analysis ,26D10 ,Mathematics - Abstract
In this paper, we establish some Hermite-Hadamard-Fejer type inclusions for the product of two co-ordinated convex interval-valued functions. These inclusions are generalizations of some results given in earlier works. Natural Science Foundation of ChinaNational Natural Science Foundation of China (NSFC) [61673169, 11301127, 11701176, 11626101, 11601485, 11971241] The work was supported by the Natural Science Foundation of China (Grant Nos. 61673169, 11301127, 11701176, 11626101, 11601485, 11971241). WOS:000619775200002 2-s2.0-85101090255
- Published
- 2021
10. Integration of oscillatory and subanalytic functions
- Author
-
Cluckers, Raf, Comte, Georges, Miller, Daniel J., Rolin, Jean-Philippe, Servi, Tamara, Miller, Daniel, Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Department of mathematics, Catholic University of Leuven - Katholieke Universiteit Leuven (KU Leuven), Laboratoire de Mathématiques (LAMA), Centre National de la Recherche Scientifique (CNRS)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), Department of Mathematics & Economics [Emporia] (MathEcon), Emporia State University, Institut de Mathématiques de Bourgogne [Dijon] (IMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB), Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG (UMR_7586)), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Cluckers's work was partially supported by the European Research Council (ERC) under the European Community's Seventh Framework Programme FP7/2007-2013 with ERC grant 615722 MOTMELSUM and by the Laboratoire d'Excellence Centre Europeen pour les Mathematiques, la Physique, et Leurs Interactions grant ANR-11-LABX-0007-01. Comte's work was partially supported by Agence Nationale de la Recherche grants ANR-15-CE40-0008 and ANR-11-BS01-0009 STAAVF. Rolin's work was partially supported by ANR-11-BS01-0009 STAAVF., ANR-11-LABX-0007,CEMPI,Centre Européen pour les Mathématiques, la Physique et leurs Interactions(2011), ANR-15-CE40-0008,Défigéo,Définissabilité en géométrie non archimédienne(2015), ANR-11-BS01-0009,STAAVF,Singularités de Trajectoires de Champs de Vecteurs Analytiques et Algébriques(2011), European Project: 615722,EC:FP7:ERC,ERC-2013-CoG,MOTMELSUM(2014), Université de Lille, Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS), Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS), Université de Bourgogne (UB), Université de Bourgogne (UB)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS), ANR-17-CE40-0023,LISA,Géométrie Lipschitz des singularités(2017), Université de Bourgogne (UB)-Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Virginia Commonwealth University (VCU), and Université de Bourgogne (UB)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Pure mathematics ,Class (set theory) ,26B15, 14P15, 32B20, 42B20, 42A38 (Primary) 03C64, 14P10, 33B10 (Secondary) ,Singularity theory ,General Mathematics ,Oscillation index ,Stability (learning theory) ,o-minimality ,PREPARATION THEOREM ,Uniformly distributed functions ,32B20 ,01 natural sciences ,33B10 ,symbols.namesake ,Mathematics - Algebraic Geometry ,0103 physical sciences ,Classical Analysis and ODEs (math.CA) ,FOS: Mathematics ,Oscillatory integrals ,0101 mathematics ,[MATH]Mathematics [math] ,42A38 ,Algebraic Geometry (math.AG) ,Constructible functions ,Mathematics ,03C64 ,Science & Technology ,010102 general mathematics ,Preparation theorems ,MSC ,Primary 26B15: Integration: length, area, volume [See also 28A75, 51M25]Secondary: 03C64: Model theory of ordered structures ,o-minimality 14P15: Real analytic and semianalytic sets [See also 32B20, 32C05] 32B20: Semi-analytic sets and subanalytic sets [See also 14P15] 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42A38: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type 14P10: Semialgebraic sets and related spaces 33B10: Exponential and trigonometric functions ,Mathematics - Logic ,Families of exponential periods ,Stability under integration ,Exponential function ,Fourier transforms ,26B15 ,14P15 ,Mathematics::Logic ,Fourier transform ,Mathematics - Classical Analysis and ODEs ,Physical Sciences ,symbols ,010307 mathematical physics ,14P10 ,[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] ,42B20 ,Logic (math.LO) ,Globally subanalytic functions - Abstract
We prove the stability under integration and under Fourier transform of a concrete class of functions containing all globally subanalytic functions and their complex exponentials. This paper extends the investigation started in [J.-M. Lion, J.-P. Rolin: "Volumes, feuilles de Rolle de feuilletages analytiques et th\'eor\`eme de Wilkie" Ann. Fac. Sci. Toulouse Math. (6) 7 (1998), no. 1, 93-112] and [R. Cluckers, D. J. Miller: "Stability under integration of sums of products of real globally subanalytic functions and their logarithms" Duke Math. J. 156 (2011), no. 2, 311-348] to an enriched framework including oscillatory functions. It provides a new example of fruitful interaction between analysis and singularity theory., Comment: Final version. Accepted for publication in Duke Math. Journal. Changes in proofs: from Section 6 to the end, we now use the theory of continuously uniformly distributed modulo 1 functions that provides a uniform technical point of view in the proofs of limit statements
- Published
- 2018
11. Gauge-measurable functions
- Author
-
Ponce, Augusto C., Van Schaftingen, Jean, and UCL - SST/IRMP - Institut de recherche en mathématique et physique
- Subjects
Lebesgue integral ,High Energy Physics::Lattice ,Kurzweil-Henstock integral ,generalized Riemann integral ,measurable function ,26B15 ,Mathematics - Classical Analysis and ODEs ,gauge integral ,gauge ,Classical Analysis and ODEs (math.CA) ,FOS: Mathematics ,28A20 ,28A05 ,28A20, 28A05, 26B15 - Abstract
In 1973, E. J. McShane introduced an alternative definition of the Lebesgue integral based on Riemann sums, where gauges are used to decide what tagged partitions are allowed. Such an approach does not require any preliminary knowledge of Measure Theory. We investigate in this paper a definition of measurable functions also based on gauges. Its relation to the gauge-integrable functions that satisfy McShane’s definition is obtained using elementary tools from Real Analysis. We show in particular a dominated integration property of gauge-measurable functions.
- Published
- 2017
12. A Generalization of the arctg function
- Author
-
Pla, Juan
- Subjects
26B15 ,Mathematics - Classical Analysis and ODEs ,Classical Analysis and ODEs (math.CA) ,FOS: Mathematics - Abstract
In this paper we define a family of continuous functions of an arbitrary number of variables, and prove that they all satisfy a generalization of one of the classical functional equations of the inverse tangent function.
- Published
- 2015
Discovery Service for Jio Institute Digital Library
For full access to our library's resources, please sign in.