Exponential trigonometric convex functions and Hermite-Hadamard type inequalities
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Mahir Kadakal
und
Mohamed Jleli
Abstract
In this manuscript, we introduce and study the concept of exponential trigonometric convex functions and their some algebraic properties. We obtain Hermite-Hadamard type inequalities for the newly introduced class of functions. We also obtain some refinements of the Hermite-Hadamard inequality for functions whose first derivative in absolute value, raised to a certain power which is greater than one, respectively at least one, is exponential trigonometric convex function. It has been shown that the result obtained with Hölder-İşcan and improved power-mean integral inequalities give better approximations than that obtained with Hölder and improved power-mean integral inequalities.
M. Jleli is supported by the Researchers Supporting Project RSP-2020/57, King Saud University, Riyadh, Saudi Arabia.
Acknowledgement
M. Jleli is supported by the Researchers Supporting Project RSP-2020/57, King Saud University, Riyadh, Saudi Arabia.
(Communicated by Tomasz Natkaniec)
References
[1] Bombardelli, M.—Varošanec, S.: Properties ofh-convex functions related to the Hermite-Hadamard-Fejér inequalities, Comput. Math. Appl. 58 (2009), 1869–1877.10.1016/j.camwa.2009.07.073Suche in Google Scholar
[2] Dragomir, S. S.—Agarwal, R. P.: Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett. 11 (1998), 91–95.10.1016/S0893-9659(98)00086-XSuche in Google Scholar
[3] Dragomir, S. S.—Pearce, C. E. M.: Selected Topics on Hermite-Hadamard Inequalities and Its Applications, RGMIA Monograph, 2002.Suche in Google Scholar
[4] Dragomir, S. S.—Pečarić, J.—Persson, L. E.: Some inequalities of Hadamard type, Soochow J. Math. 21(3) (2001), 335–341.Suche in Google Scholar
[5] Hadamard, J.: Étude sur les propriétés des fonctions entières en particulier ďune fonction considérée par Riemann, J. Math. Pures Appl. 58 (1893), 171–215.Suche in Google Scholar
[6] İşcan, İ.: New refinements for integral and sum forms of Hölder inequality, J. Inequal. Appl. 2019 (2019), Art. ID 304.10.1186/s13660-019-2258-5Suche in Google Scholar
[7] İşcan, İ.—Kunt, M.: Hermite-Hadamard-Fejer type inequalities for quasi-geometrically convex functions via fractional integrals, J. Math. 2016 (2016), Art. ID 6523041.10.1155/2016/6523041Suche in Google Scholar
[8] Kadakal, H.: Hermite-Hadamard type inequalities for trigonometrically convex functions, Sci. Stud. Res. Ser. Math. Inform. 28(2) (2018), 19–28.10.18514/MMN.2018.2066Suche in Google Scholar
[9] Kadakal, H.: New inequalities for stronglyr-convex functions, J. Funct. Spaces 2019 (2019), Art. Id. 1219237.10.1155/2019/1219237Suche in Google Scholar
[10] Kadakal, M.—İşcan, İ.—Kadakal, H.—BEKAR, K.: On improvements of some integral inequalities, Miskolc Math. Notes, submitted.Suche in Google Scholar
[11] Kadakal, M.—Kadakal, H.—İşcan, İ.: Some new integral inequalities forn-times differentiables-convex functions in the first sense, Turkish Journal of Analysis and Number Theory 5(2) (2017), 63–68.10.12691/tjant-5-2-4Suche in Google Scholar
[12] Maden, S.—Kadakal, H.—Kadakal, M.—İşcan, İ.: Some new integral inequalities forn-times differentiable convex and concave functions, J. Nonlinear Sci. Appl. 10(12) (2017), 6141–6148.10.22436/jnsa.010.12.01Suche in Google Scholar
[13] Özcan, S.: Some integral inequalities for harmonically (α, s)-convex functions, J. Funct. Spaces 2019 (2019), Art. ID 2394021.10.1155/2019/2394021Suche in Google Scholar
[14] Özcan, S.—İşcan, İ.: Some new Hermite-Hadamard type inequalities fors-convex functions and their applications, J. Inequal. Appl. 2019 (2019), Art. ID 201.10.1186/s13660-019-2151-2Suche in Google Scholar
[15] Varošanec, S.: Onh-convexity, J. Math. Anal. Appl. 326 (2007), 303–311.10.1016/j.jmaa.2006.02.086Suche in Google Scholar
[16] Zabandan, G.: A new refinement of the Hermite-Hadamard inequality for convex functions, J. Inequal. Pure Appl. Math. 10(2) (2009), Art. ID 45.Suche in Google Scholar
© 2021 Mathematical Institute Slovak Academy of Sciences
Artikel in diesem Heft
- Regular papers
- Prof. RNDr. Ing. Lubomír Kubáček, DrSc., Dr.h.c. –Nonagenarian
- Doc. RNDr. Roman Frič, DrSc. passed away
- Outer and inner approximations in quantum spaces
- Linear derivations on Banach *-algebras
- New fractional order discrete Grüss type inequality
- Exponential trigonometric convex functions and Hermite-Hadamard type inequalities
- Generalized Minkowski type inequality for pseudo-integral
- Study of the Q-spiral-like functions of complex order
- Radius of starlikeness of certain analytic functions
- Successive approximations for a differential equation in a Banach space via Constantin condition
- Approximation of the multi-m-Jensen-quadratic mappings and a fixed point approach
- Oscillation and asymptotic behavior of a higher-order neutral delay difference equation with variable delays under Δm
- Sequence selection properties in Cp(X) with the double ideals
- On the paranormed Nörlund difference sequence space of fractional order and geometric properties
- On certain Diophantine equations concerning the area of right triangles
- Weighted projective Ricci curvature in Finsler geometry
- Euler classes of vector bundles over manifolds
- A new generalized Lindley-Weibull class of distributions: Theory, properties and applications
- Dynamical behaviors of a prey-predator model with foraging arena scheme in polluted environments
- The (α, β)-ramification invariants of a number field
Artikel in diesem Heft
- Regular papers
- Prof. RNDr. Ing. Lubomír Kubáček, DrSc., Dr.h.c. –Nonagenarian
- Doc. RNDr. Roman Frič, DrSc. passed away
- Outer and inner approximations in quantum spaces
- Linear derivations on Banach *-algebras
- New fractional order discrete Grüss type inequality
- Exponential trigonometric convex functions and Hermite-Hadamard type inequalities
- Generalized Minkowski type inequality for pseudo-integral
- Study of the Q-spiral-like functions of complex order
- Radius of starlikeness of certain analytic functions
- Successive approximations for a differential equation in a Banach space via Constantin condition
- Approximation of the multi-m-Jensen-quadratic mappings and a fixed point approach
- Oscillation and asymptotic behavior of a higher-order neutral delay difference equation with variable delays under Δm
- Sequence selection properties in Cp(X) with the double ideals
- On the paranormed Nörlund difference sequence space of fractional order and geometric properties
- On certain Diophantine equations concerning the area of right triangles
- Weighted projective Ricci curvature in Finsler geometry
- Euler classes of vector bundles over manifolds
- A new generalized Lindley-Weibull class of distributions: Theory, properties and applications
- Dynamical behaviors of a prey-predator model with foraging arena scheme in polluted environments
- The (α, β)-ramification invariants of a number field
