Research Article
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Year 2021, , 287 - 293, 31.12.2021
https://doi.org/10.47000/tjmcs.925182

Abstract

References

  • [1] Abramowitz, M., Stegun, I.A., (Eds), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series 55, Washington, 1970.
  • [2] Adilov, G., Rubinov, A.M., $B-$convex sets and functions. Numerical Functional Analysis and Optimization, 27(3-4)(2006), 237–257.
  • [3] Adilov, G., Yesilce, I., On Generalizations of the concept of convexity, Hacettepe Journal of Mathematics and Statistics, 41(5)(2012), 723–730.
  • [4] Adilov, G., Kemali, S., Abstract convexity and Hermite-Hadamard type inequalities, Journal of Inequalities and Applications, 2009(2009), 943534.
  • [5] Alomari, M.W., Darus, M., Kirmaci, U.S., Some inequalities of Hermite-Hadamard type for s-convex functions, Acta Mathematica Scientia, 31(4)(2011), 1643–1652.
  • [6] 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(5)(1998), 91–95.
  • [7] Dragomir, S.S., Pierce, C.E.M., On some inequalities for differentiable convex functions and applications, preprint, (2000).
  • [8] Dragomir, S.S., Pierce, C.E.M., Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA, Victoria University, 2000.
  • [9] Dragomir S.S., Fitzpatrick, S., The Hadamard’s inequality for s-convex functions in the second sense, Demonstratio Math., 32(4)(1999), 687–696.
  • [10] Eken, Z., Sezer, S., Tınaztepe, G., Adilov, G., s-convex functions in the fourth sense and their some properties. Submitted.
  • [11] Hudzik, H., Maligranda, L., Some remarks on s-convex functions. Aequ. Math. 48(1994), 100–111.
  • [12] Khan, M., Hanif, M.A., Khan, A.H., et al, Association of Jensen’s inequality for s-convex function with Csiszar divergence, J Inequal 162(2019).
  • [13] Kırmacı, U.S., Bakula, M.K., Ozdemir, M.E., Pecaric, J., Hadamard-type inequalities for s-convex functions, Appl. Math. Comput., 193(2007), 26–35.
  • [14] Kemali, S., Sezer, S., Tınaztepe, G., Adilov, G., s-Convex function in the third sense, Korean J. Math., 29(3)(2021), 593-602.
  • [15] Kemali, S., Yesilce, I., Adilov, G., $B$-Convexity, $B^{-1}$-Convexity, and their comparison, Numerical Functional Analysis and Optimization, 36(2)(2015), 133–146.
  • [16] Orlicz, W., A note on modular spaces I. Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys, 9(1961), 157–162.
  • [17] Özcan, S., İşcan, I., Some new Hermite–Hadamard type inequalities for s-convex functions and their applications, Journal of Inequalities and Applications, Article, 201, (2019).
  • [18] Pearce C.E.M., Pecaric, J., Inequalities for differentiable mappings with application to special means and quadrature formula, Applied Mathematics Letters 13(2)(2000), 51–55.
  • [19] Sezer, S., Eken, Z., Tınaztepe, G., Adilov, G., p-Convex functions and some of their properties, Numerical Functional Analysis and Optimization, 42(4)(2021), 443–459.
  • [20] Sezer, S., The Hermite-Hadamard inequality for s-Convex functions in the third sense AIMS Mathematics, 6(7), (2021), 7719–7732.
  • [21] Tinaztepe, G. Yesilce, I., Adilov, G., Separation of $B^{-1}$-convex sets by $B^{-1}$-measurable Maps, Journal of Convex Analysis, 21(2)(2014), 571–580.
  • [22] Yeşilce, İ., Adilov, G., Hermite-Hadamard inequalities for $B$-convex and $B^{-1}$-convex functions. International Journal of Nonlinear Analysis and Applications, 8(1)(2017), 225–233.
  • [23] Zhang, K.S., Wan, J.P., p-Convex functions and their properties, Pure and Applied Mathematics, 1(23)2007), 130–133.

Hermite-Hadamard Type Inequality for s-Convex Functions in the Fourth Sense

Year 2021, , 287 - 293, 31.12.2021
https://doi.org/10.47000/tjmcs.925182

Abstract

In this study, firstly, Hermite-Hadamard type inequalities are examined for functions whose first derivative is $s$-convex functions in the fourth sense. In addition, Hermite-Hadamard type inequalities are examined for functions whose second derivative is $s$-convex functions in the fourth sense. Finally, some application examples including special tools and digamma functions are presented.

References

  • [1] Abramowitz, M., Stegun, I.A., (Eds), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series 55, Washington, 1970.
  • [2] Adilov, G., Rubinov, A.M., $B-$convex sets and functions. Numerical Functional Analysis and Optimization, 27(3-4)(2006), 237–257.
  • [3] Adilov, G., Yesilce, I., On Generalizations of the concept of convexity, Hacettepe Journal of Mathematics and Statistics, 41(5)(2012), 723–730.
  • [4] Adilov, G., Kemali, S., Abstract convexity and Hermite-Hadamard type inequalities, Journal of Inequalities and Applications, 2009(2009), 943534.
  • [5] Alomari, M.W., Darus, M., Kirmaci, U.S., Some inequalities of Hermite-Hadamard type for s-convex functions, Acta Mathematica Scientia, 31(4)(2011), 1643–1652.
  • [6] 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(5)(1998), 91–95.
  • [7] Dragomir, S.S., Pierce, C.E.M., On some inequalities for differentiable convex functions and applications, preprint, (2000).
  • [8] Dragomir, S.S., Pierce, C.E.M., Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA, Victoria University, 2000.
  • [9] Dragomir S.S., Fitzpatrick, S., The Hadamard’s inequality for s-convex functions in the second sense, Demonstratio Math., 32(4)(1999), 687–696.
  • [10] Eken, Z., Sezer, S., Tınaztepe, G., Adilov, G., s-convex functions in the fourth sense and their some properties. Submitted.
  • [11] Hudzik, H., Maligranda, L., Some remarks on s-convex functions. Aequ. Math. 48(1994), 100–111.
  • [12] Khan, M., Hanif, M.A., Khan, A.H., et al, Association of Jensen’s inequality for s-convex function with Csiszar divergence, J Inequal 162(2019).
  • [13] Kırmacı, U.S., Bakula, M.K., Ozdemir, M.E., Pecaric, J., Hadamard-type inequalities for s-convex functions, Appl. Math. Comput., 193(2007), 26–35.
  • [14] Kemali, S., Sezer, S., Tınaztepe, G., Adilov, G., s-Convex function in the third sense, Korean J. Math., 29(3)(2021), 593-602.
  • [15] Kemali, S., Yesilce, I., Adilov, G., $B$-Convexity, $B^{-1}$-Convexity, and their comparison, Numerical Functional Analysis and Optimization, 36(2)(2015), 133–146.
  • [16] Orlicz, W., A note on modular spaces I. Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys, 9(1961), 157–162.
  • [17] Özcan, S., İşcan, I., Some new Hermite–Hadamard type inequalities for s-convex functions and their applications, Journal of Inequalities and Applications, Article, 201, (2019).
  • [18] Pearce C.E.M., Pecaric, J., Inequalities for differentiable mappings with application to special means and quadrature formula, Applied Mathematics Letters 13(2)(2000), 51–55.
  • [19] Sezer, S., Eken, Z., Tınaztepe, G., Adilov, G., p-Convex functions and some of their properties, Numerical Functional Analysis and Optimization, 42(4)(2021), 443–459.
  • [20] Sezer, S., The Hermite-Hadamard inequality for s-Convex functions in the third sense AIMS Mathematics, 6(7), (2021), 7719–7732.
  • [21] Tinaztepe, G. Yesilce, I., Adilov, G., Separation of $B^{-1}$-convex sets by $B^{-1}$-measurable Maps, Journal of Convex Analysis, 21(2)(2014), 571–580.
  • [22] Yeşilce, İ., Adilov, G., Hermite-Hadamard inequalities for $B$-convex and $B^{-1}$-convex functions. International Journal of Nonlinear Analysis and Applications, 8(1)(2017), 225–233.
  • [23] Zhang, K.S., Wan, J.P., p-Convex functions and their properties, Pure and Applied Mathematics, 1(23)2007), 130–133.
There are 23 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Serap Kemali 0000-0001-5804-4127

Publication Date December 31, 2021
Published in Issue Year 2021

Cite

APA Kemali, S. (2021). Hermite-Hadamard Type Inequality for s-Convex Functions in the Fourth Sense. Turkish Journal of Mathematics and Computer Science, 13(2), 287-293. https://doi.org/10.47000/tjmcs.925182
AMA Kemali S. Hermite-Hadamard Type Inequality for s-Convex Functions in the Fourth Sense. TJMCS. December 2021;13(2):287-293. doi:10.47000/tjmcs.925182
Chicago Kemali, Serap. “Hermite-Hadamard Type Inequality for S-Convex Functions in the Fourth Sense”. Turkish Journal of Mathematics and Computer Science 13, no. 2 (December 2021): 287-93. https://doi.org/10.47000/tjmcs.925182.
EndNote Kemali S (December 1, 2021) Hermite-Hadamard Type Inequality for s-Convex Functions in the Fourth Sense. Turkish Journal of Mathematics and Computer Science 13 2 287–293.
IEEE S. Kemali, “Hermite-Hadamard Type Inequality for s-Convex Functions in the Fourth Sense”, TJMCS, vol. 13, no. 2, pp. 287–293, 2021, doi: 10.47000/tjmcs.925182.
ISNAD Kemali, Serap. “Hermite-Hadamard Type Inequality for S-Convex Functions in the Fourth Sense”. Turkish Journal of Mathematics and Computer Science 13/2 (December 2021), 287-293. https://doi.org/10.47000/tjmcs.925182.
JAMA Kemali S. Hermite-Hadamard Type Inequality for s-Convex Functions in the Fourth Sense. TJMCS. 2021;13:287–293.
MLA Kemali, Serap. “Hermite-Hadamard Type Inequality for S-Convex Functions in the Fourth Sense”. Turkish Journal of Mathematics and Computer Science, vol. 13, no. 2, 2021, pp. 287-93, doi:10.47000/tjmcs.925182.
Vancouver Kemali S. Hermite-Hadamard Type Inequality for s-Convex Functions in the Fourth Sense. TJMCS. 2021;13(2):287-93.