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2021 | OriginalPaper | Buchkapitel

New Trapezoid Type Inequalities for Generalized Exponentially Strongly Convex Functions

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Abstract

By using a new general identity and introducing some very general new notions of generalized exponentially strongly convex functions, new trapezoid type inequalities are established. We apply these inequalities to provide approximations for the integral of a real valued function. Approximations for some new weighted means of two positive numbers are also obtained.

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Literatur
1.
Zurück zum Zitat M.U. Anwar, M.A. Noor, K.I. Noor, Hermite-Hadarmard inequalities for exponentially convex functions. Appl. Math. Inf. Sci. 12(2), 405–409 (2018)MathSciNetCrossRef M.U. Anwar, M.A. Noor, K.I. Noor, Hermite-Hadarmard inequalities for exponentially convex functions. Appl. Math. Inf. Sci. 12(2), 405–409 (2018)MathSciNetCrossRef
2.
Zurück zum Zitat J.C. Kuang, Applied Inequalities, 4th edn. (Shangdong Science and Technology Press, Jinan, 2010) (in Chinese) J.C. Kuang, Applied Inequalities, 4th edn. (Shangdong Science and Technology Press, Jinan, 2010) (in Chinese)
3.
Zurück zum Zitat D.S. Mitrinovic, J.E. Pecaric, A.M. Fink, Classical and New Inequalties in Analysis (Kluwer Academic Publishers, Dordrecht/Boston/London, 1993)MATHCrossRef D.S. Mitrinovic, J.E. Pecaric, A.M. Fink, Classical and New Inequalties in Analysis (Kluwer Academic Publishers, Dordrecht/Boston/London, 1993)MATHCrossRef
5.
Zurück zum Zitat I. Iscan, S. Wu, Hermite-Hadamard type inequalities for harmonically convex functions via fractional integrals. Appl. Math. Comput. 238, 237–244 (2014)MathSciNetMATH I. Iscan, S. Wu, Hermite-Hadamard type inequalities for harmonically convex functions via fractional integrals. Appl. Math. Comput. 238, 237–244 (2014)MathSciNetMATH
6.
Zurück zum Zitat S.S. Dragomir, R.P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula. Appl. Math. Lett. 11, 91–95 (1998)MathSciNetMATHCrossRef S.S. Dragomir, R.P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula. Appl. Math. Lett. 11, 91–95 (1998)MathSciNetMATHCrossRef
7.
8.
Zurück zum Zitat N. Mehreen, M. Anwar, Hermite-Hadarmard type inequalitis for exponentially p −convex functions and exponentially s −convex functions in the second sense with applications. J. Inequal. Appl. Article number 92 (2019) N. Mehreen, M. Anwar, Hermite-Hadarmard type inequalitis for exponentially p −convex functions and exponentially s −convex functions in the second sense with applications. J. Inequal. Appl. Article number 92 (2019)
9.
Zurück zum Zitat M.A. Latif, Estimates of Hermite-Hadamard inequality for twice differentiable harmonically convex functions with applications. Punjab Univ. J. Math. (Lahore) 50(1), 1–13 (2018) M.A. Latif, Estimates of Hermite-Hadamard inequality for twice differentiable harmonically convex functions with applications. Punjab Univ. J. Math. (Lahore) 50(1), 1–13 (2018)
10.
Zurück zum Zitat S.S. Dragomir, Inequalities for the Riemann-Stieltjes integral of (p, q) −H-dominated integrators with applications. Appl. Math. E-Notes 15, 243–260 (2015)MathSciNetMATH S.S. Dragomir, Inequalities for the Riemann-Stieltjes integral of (p, q) −H-dominated integrators with applications. Appl. Math. E-Notes 15, 243–260 (2015)MathSciNetMATH
11.
Zurück zum Zitat K.S. Zhang, J.P. Wan, p −convex functions and their properties. Pure Appl. Math. 23(1), 130–133 (2007) K.S. Zhang, J.P. Wan, p −convex functions and their properties. Pure Appl. Math. 23(1), 130–133 (2007)
12.
Zurück zum Zitat Z.B. Fang, R.J. Shi, On (p, h) −convex function and some integral inequalities. J. Inequal. Appl. 45 (2004) Z.B. Fang, R.J. Shi, On (p, h) −convex function and some integral inequalities. J. Inequal. Appl. 45 (2004)
13.
Zurück zum Zitat M.A. Noor, K.I. Noor, M.U. Awan, Some new estimates of Hermite-Hadamard inequalities via harmonically r −convex functions. LEMATEMATICHE 7(2), 117–127 (2016)MathSciNetMATH M.A. Noor, K.I. Noor, M.U. Awan, Some new estimates of Hermite-Hadamard inequalities via harmonically r −convex functions. LEMATEMATICHE 7(2), 117–127 (2016)MathSciNetMATH
14.
Zurück zum Zitat S.S. Dragomir, C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequality (Victoria University Press, Victoria (Australia), 2000) S.S. Dragomir, C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequality (Victoria University Press, Victoria (Australia), 2000)
15.
Zurück zum Zitat M. Alomari, M. Darus, S.S. Dragomir, New inequalities of Hermite-Hadarmard type for functions whose second derivatives absolute values are quasi-convex. Tamkang J. Math. 41(4), 353–359 (2010)MathSciNetMATHCrossRef M. Alomari, M. Darus, S.S. Dragomir, New inequalities of Hermite-Hadarmard type for functions whose second derivatives absolute values are quasi-convex. Tamkang J. Math. 41(4), 353–359 (2010)MathSciNetMATHCrossRef
16.
17.
Zurück zum Zitat S.S. Dragomir, On some new inequalities of Hermite-Hadamard type for functions m −convex functions. Tamkang J. Math. 33(1), 55–65 (2002)MathSciNetMATHCrossRef S.S. Dragomir, On some new inequalities of Hermite-Hadamard type for functions m −convex functions. Tamkang J. Math. 33(1), 55–65 (2002)MathSciNetMATHCrossRef
18.
Zurück zum Zitat J.C. Kuang, Some recent developments in the theory of convex functions. J. Guangdong Univ. Edu. 38(3), 14–24 (2018) J.C. Kuang, Some recent developments in the theory of convex functions. J. Guangdong Univ. Edu. 38(3), 14–24 (2018)
19.
Zurück zum Zitat B.T. Polyak, Existence theorems and convergence of minimizing sequences in extremum problems with restrictions. Sov. Math. Dokl. 7, 7–75 (1966) B.T. Polyak, Existence theorems and convergence of minimizing sequences in extremum problems with restrictions. Sov. Math. Dokl. 7, 7–75 (1966)
21.
Zurück zum Zitat S.S. Dragomir, Integral inequalities of Jensen type for λ −convex functions. MATEMATUUKH BECHUK 68(1), 45–57 (2016)MathSciNetMATH S.S. Dragomir, Integral inequalities of Jensen type for λ −convex functions. MATEMATUUKH BECHUK 68(1), 45–57 (2016)MathSciNetMATH
22.
Zurück zum Zitat K. Nikodem, On strongly convex functions and related classes of functions, in Handbook of Functional Equations: Functional Inequalities. Springer Optimizations and Its Applications, vol. 95 (Springer, Springer-Verlag, Berlin-Heidelberg–New York, 2014), pp. 365–405 K. Nikodem, On strongly convex functions and related classes of functions, in Handbook of Functional Equations: Functional Inequalities. Springer Optimizations and Its Applications, vol. 95 (Springer, Springer-Verlag, Berlin-Heidelberg–New York, 2014), pp. 365–405
23.
Zurück zum Zitat P. Cerone, S.S. Dragomir, E. Kikianty, Multiplicative Ostrowski and trapezoid inequalities, in Handbook of Functional Equations: Functional Inequalities. Springer optimizations and its applications, Vol. 95 (Springer, New York, 2014), pp. 57–73 P. Cerone, S.S. Dragomir, E. Kikianty, Multiplicative Ostrowski and trapezoid inequalities, in Handbook of Functional Equations: Functional Inequalities. Springer optimizations and its applications, Vol. 95 (Springer, New York, 2014), pp. 57–73
24.
Zurück zum Zitat M. Adamek, On a problem connected with strongly convex functions. Math. Inequal. Appl. 19(4), 1287–1293 (2016)MathSciNetMATH M. Adamek, On a problem connected with strongly convex functions. Math. Inequal. Appl. 19(4), 1287–1293 (2016)MathSciNetMATH
25.
Zurück zum Zitat B. Samet, On an implicit convexity concept and some integral inequalities. J. Inequal. Appl. 308 (2016) B. Samet, On an implicit convexity concept and some integral inequalities. J. Inequal. Appl. 308 (2016)
26.
Zurück zum Zitat P.O. Mohammed, M.Z. Sarikya, Hermite-Hadamard type inequalities for F −convex function involving fractional integrals. J. Inequal. Appl. 359 (2018) P.O. Mohammed, M.Z. Sarikya, Hermite-Hadamard type inequalities for F −convex function involving fractional integrals. J. Inequal. Appl. 359 (2018)
27.
Zurück zum Zitat S.M. Kang, G. Farid, W. Nazeer, S. Mehmood, (h −m) −convex functions and associated fractional Hadamard and Fej\(\acute {e}\)r-Hadamard inequalities via an extended generalized Mittag-Leffler function. J. Inequal. Appl. 78 (2019) S.M. Kang, G. Farid, W. Nazeer, S. Mehmood, (h −m) −convex functions and associated fractional Hadamard and Fej\(\acute {e}\)r-Hadamard inequalities via an extended generalized Mittag-Leffler function. J. Inequal. Appl. 78 (2019)
28.
Zurück zum Zitat V.G. Mihesan, A generalization of the convexity. Seminar on functional equations. Approx. and Convex., Cluj-Napoca(Romania) (1993) V.G. Mihesan, A generalization of the convexity. Seminar on functional equations. Approx. and Convex., Cluj-Napoca(Romania) (1993)
29.
Zurück zum Zitat M.A. Noor, M.U. Awan, K.I. Nook, T.M. Rassias, On (α, m, h) −convexity. Appl. Math. Inf. Sci. 12(1), 145–150 (2018)MathSciNetCrossRef M.A. Noor, M.U. Awan, K.I. Nook, T.M. Rassias, On (α, m, h) −convexity. Appl. Math. Inf. Sci. 12(1), 145–150 (2018)MathSciNetCrossRef
30.
Zurück zum Zitat Y.C. Kwun, M.S. Saleem, M. Ghafoor, W. Nazeer, S.M. Kang, Hermite-Hadamard -type inequalities for functions whose derivatives are η −convex via fractional integrals. J. Inequal. Appl. 44 (2019) Y.C. Kwun, M.S. Saleem, M. Ghafoor, W. Nazeer, S.M. Kang, Hermite-Hadamard -type inequalities for functions whose derivatives are η −convex via fractional integrals. J. Inequal. Appl. 44 (2019)
31.
Zurück zum Zitat S. Dragomir, Operator Inequalities of Ostrowski and Trapezoidal Type (Springer, New York, 2012)MATHCrossRef S. Dragomir, Operator Inequalities of Ostrowski and Trapezoidal Type (Springer, New York, 2012)MATHCrossRef
32.
Zurück zum Zitat I. Iscan, Hermite-Hadamard type inequalities for p −convex functions. Int. J. Anal. Appl. 11(2), 137–145 (2016)MathSciNetMATH I. Iscan, Hermite-Hadamard type inequalities for p −convex functions. Int. J. Anal. Appl. 11(2), 137–145 (2016)MathSciNetMATH
33.
Zurück zum Zitat M. Abramowitz, I.A. Stegum (eds.), Handbook of Mathematical Functions (Dover Publications, Inc. New York, 1972) M. Abramowitz, I.A. Stegum (eds.), Handbook of Mathematical Functions (Dover Publications, Inc. New York, 1972)
Metadaten
Titel
New Trapezoid Type Inequalities for Generalized Exponentially Strongly Convex Functions
verfasst von
Kuang Jichang
Copyright-Jahr
2021
DOI
https://doi.org/10.1007/978-3-030-60622-0_15

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