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Hermite-Hadamard Type Inequalities for the Functions Whose Absolute Values of First Derivatives are $p$-Convex

Yıl 2021, Cilt 4, Sayı 2, 88 - 99, 01.06.2021
https://doi.org/10.33401/fujma.881979

Öz

In this paper, we extend some estimates of a Hermite-Hadamard type inequality for functions whose absolute values of the first derivatives are $p$-convex. By means of the obtained inequalities, some bound functions involving beta functions and hypergeometric functions are derived as applications. Also, we suggest an upper bound for error in numerical integration of $p$-convex functions via composite trapezoid rule.

Kaynakça

  • [1] G. Adilov, I. Yesilce, On generalizations of the concept of convexity, Hacet. J. Math. Stat., 41(5) (2012), 723-730.
  • [2] G. Adilov, I. Yesilce, B^-11-convex functions, J. Convex Anal., 24(2) (2017), 505-517.
  • [3] G. R. Adilov, S. Kemali, Abstract convexity, and Hermite-Hadamard type inequalities, J. Inequal. Appl., 2009 (2009), Article ID 943534, 13 pages, DOI:10.1155/2009/943534.
  • [4] W. Briec, C. Horvath, B-convexity, Optimization, 53(2) (2004), 103-127.
  • [5] S. I. Butt, A. Kashuri, M. Tariq, J. Nasir, A. Aslam, W. Gao, n–polynomial exponential type p–convex function with some related inequalities and their applications, Heliyon, 6(11) (2020), e05420.
  • [6] Z. B. Fang, R. Shi, On the (p,h)-convex function and some integral inequalities, J. Inequal. Appl., 45 (2014), 1-16.
  • [7] S. Kemali, G. Tınaztepe, G. Adilov, New type inequalities for B^-11-convex functions involving Hadamard fractional integral, Ser. Math. Inform., 33(5) (2018), 697-704.
  • [8] S. Kemali, I. Yesilce, G. Adilov, B-convexity, B􀀀1-convexity, and their comparison, Numer. Funct. Anal. Optim., 36(2) (2015), 133-146.
  • [9] W. Orlicz, A note on modular spaces I, Bull. Acad. Polon. Soi., Ser. Math. Astronom Phys., 9 (1961), 157-162.
  • [10] G. Tinaztepe, I. Yesilce, G. Adilov, Separation of B^-1-convex sets by B^-1-measurable maps, J. Convex Anal., 21(2) (2014), 571-580.
  • [11] I. Yesilce, G. Adilov, Some operations on B^-1-convex sets, J. Math. Sci. Adv. Appl., 39(1) (2016), 99-104.
  • [12] I. Yesilce, Inequalities for B-convex functions via generalized fractional integrals, J. Inequal. Appl., 194 (2019), DOI 10.1186/s13660-019-2150-3.
  • [13] S. S. Dragomir, J. Pecaric, L. E. Persson, Some inequalities of Hadamard type, Soochow J. Math., 21(3) (1995), 335-341.
  • [14] S. S. Dragomir, C. Pearce, Selected topics on Hermite-Hadamard inequalities and applications, Math. Prep. Archive, 3 (2003), 463-817.
  • [15] S. S. Dragomir, R. P. Agarwal, N. S. Barnett, Inequalities for Beta and Gamma functions via some classical and new integral inequalities, J. Inequal. Appl., 5 (2000), 103–165. [16] ˙I. ˙Is¸can, Ostrowski type inequalities for p-convex functions, NTMSCI, 4(3) (2016), 140-150.
  • [17] A. Bayoumi, A. Fathy Ahmed, p-convex functions in discrete sets, Int. J. Eng. Appl. Sci., 4(10) (2017), 63-66.
  • [18] N. T. Peck, Banach-Mazur distances and projections on p-convex spaces, Math. Z., 177(1) (1981), 131-142.
  • [19] J. Bastero, J. Bernues, A. Pena, The theorems of Caratheodory and Gluskin for 0 < p < 1, Proc. Amer. Math. Soc., 123(1) (1995), 141-144.
  • [20] J. Bernu´es, A. Pena, On the shape of p-convex hulls, 0 < p < 1, Acta Math. Hungar., 74(4) (1997), 345-353.
  • [21] J. Kim, V. Yaskin, A. Zvavitch, The geometry of p-convex intersection bodies, Adv. Math., 226(6) (2011), 5320-5337.
  • [22] S. Sezer, Z. Eken, G. Tinaztepe, G. Adilov p-convex functions and some of their properties, Numer. Funct. Anal. Optim., 42(4) (2021), 443-459.
  • [23] Z. Eken, S. Kemali, G. Tınaztepe, G. Adilov, The Hermite-Hadamard inequalities for p-convex functions, Hacet. J. Math. Stat., (in press).

Yıl 2021, Cilt 4, Sayı 2, 88 - 99, 01.06.2021
https://doi.org/10.33401/fujma.881979

Öz

Kaynakça

  • [1] G. Adilov, I. Yesilce, On generalizations of the concept of convexity, Hacet. J. Math. Stat., 41(5) (2012), 723-730.
  • [2] G. Adilov, I. Yesilce, B^-11-convex functions, J. Convex Anal., 24(2) (2017), 505-517.
  • [3] G. R. Adilov, S. Kemali, Abstract convexity, and Hermite-Hadamard type inequalities, J. Inequal. Appl., 2009 (2009), Article ID 943534, 13 pages, DOI:10.1155/2009/943534.
  • [4] W. Briec, C. Horvath, B-convexity, Optimization, 53(2) (2004), 103-127.
  • [5] S. I. Butt, A. Kashuri, M. Tariq, J. Nasir, A. Aslam, W. Gao, n–polynomial exponential type p–convex function with some related inequalities and their applications, Heliyon, 6(11) (2020), e05420.
  • [6] Z. B. Fang, R. Shi, On the (p,h)-convex function and some integral inequalities, J. Inequal. Appl., 45 (2014), 1-16.
  • [7] S. Kemali, G. Tınaztepe, G. Adilov, New type inequalities for B^-11-convex functions involving Hadamard fractional integral, Ser. Math. Inform., 33(5) (2018), 697-704.
  • [8] S. Kemali, I. Yesilce, G. Adilov, B-convexity, B􀀀1-convexity, and their comparison, Numer. Funct. Anal. Optim., 36(2) (2015), 133-146.
  • [9] W. Orlicz, A note on modular spaces I, Bull. Acad. Polon. Soi., Ser. Math. Astronom Phys., 9 (1961), 157-162.
  • [10] G. Tinaztepe, I. Yesilce, G. Adilov, Separation of B^-1-convex sets by B^-1-measurable maps, J. Convex Anal., 21(2) (2014), 571-580.
  • [11] I. Yesilce, G. Adilov, Some operations on B^-1-convex sets, J. Math. Sci. Adv. Appl., 39(1) (2016), 99-104.
  • [12] I. Yesilce, Inequalities for B-convex functions via generalized fractional integrals, J. Inequal. Appl., 194 (2019), DOI 10.1186/s13660-019-2150-3.
  • [13] S. S. Dragomir, J. Pecaric, L. E. Persson, Some inequalities of Hadamard type, Soochow J. Math., 21(3) (1995), 335-341.
  • [14] S. S. Dragomir, C. Pearce, Selected topics on Hermite-Hadamard inequalities and applications, Math. Prep. Archive, 3 (2003), 463-817.
  • [15] S. S. Dragomir, R. P. Agarwal, N. S. Barnett, Inequalities for Beta and Gamma functions via some classical and new integral inequalities, J. Inequal. Appl., 5 (2000), 103–165. [16] ˙I. ˙Is¸can, Ostrowski type inequalities for p-convex functions, NTMSCI, 4(3) (2016), 140-150.
  • [17] A. Bayoumi, A. Fathy Ahmed, p-convex functions in discrete sets, Int. J. Eng. Appl. Sci., 4(10) (2017), 63-66.
  • [18] N. T. Peck, Banach-Mazur distances and projections on p-convex spaces, Math. Z., 177(1) (1981), 131-142.
  • [19] J. Bastero, J. Bernues, A. Pena, The theorems of Caratheodory and Gluskin for 0 < p < 1, Proc. Amer. Math. Soc., 123(1) (1995), 141-144.
  • [20] J. Bernu´es, A. Pena, On the shape of p-convex hulls, 0 < p < 1, Acta Math. Hungar., 74(4) (1997), 345-353.
  • [21] J. Kim, V. Yaskin, A. Zvavitch, The geometry of p-convex intersection bodies, Adv. Math., 226(6) (2011), 5320-5337.
  • [22] S. Sezer, Z. Eken, G. Tinaztepe, G. Adilov p-convex functions and some of their properties, Numer. Funct. Anal. Optim., 42(4) (2021), 443-459.
  • [23] Z. Eken, S. Kemali, G. Tınaztepe, G. Adilov, The Hermite-Hadamard inequalities for p-convex functions, Hacet. J. Math. Stat., (in press).

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Yayınlanma Tarihi Yaz
Bölüm Makaleler
Yazarlar

Sevda SEZER (Sorumlu Yazar)
AKDENİZ ÜNİVERSİTESİ
0000-0001-6448-193X
Türkiye

Yayımlanma Tarihi 1 Haziran 2021
Yayınlandığı Sayı Yıl 2021, Cilt 4, Sayı 2

Kaynak Göster

Bibtex @araştırma makalesi { fujma881979, journal = {Fundamental Journal of Mathematics and Applications}, issn = {2645-8845}, address = {}, publisher = {Fuat USTA}, year = {2021}, volume = {4}, pages = {88 - 99}, doi = {10.33401/fujma.881979}, title = {Hermite-Hadamard Type Inequalities for the Functions Whose Absolute Values of First Derivatives are \$p\$-Convex}, key = {cite}, author = {Sezer, Sevda} }
APA Sezer, S. (2021). Hermite-Hadamard Type Inequalities for the Functions Whose Absolute Values of First Derivatives are $p$-Convex . Fundamental Journal of Mathematics and Applications , 4 (2) , 88-99 . DOI: 10.33401/fujma.881979
MLA Sezer, S. "Hermite-Hadamard Type Inequalities for the Functions Whose Absolute Values of First Derivatives are $p$-Convex" . Fundamental Journal of Mathematics and Applications 4 (2021 ): 88-99 <https://dergipark.org.tr/tr/pub/fujma/issue/62527/881979>
Chicago Sezer, S. "Hermite-Hadamard Type Inequalities for the Functions Whose Absolute Values of First Derivatives are $p$-Convex". Fundamental Journal of Mathematics and Applications 4 (2021 ): 88-99
RIS TY - JOUR T1 - Hermite-Hadamard Type Inequalities for the Functions Whose Absolute Values of First Derivatives are $p$-Convex AU - Sevda Sezer Y1 - 2021 PY - 2021 N1 - doi: 10.33401/fujma.881979 DO - 10.33401/fujma.881979 T2 - Fundamental Journal of Mathematics and Applications JF - Journal JO - JOR SP - 88 EP - 99 VL - 4 IS - 2 SN - 2645-8845- M3 - doi: 10.33401/fujma.881979 UR - https://doi.org/10.33401/fujma.881979 Y2 - 2021 ER -
EndNote %0 Fundamental Journal of Mathematics and Applications Hermite-Hadamard Type Inequalities for the Functions Whose Absolute Values of First Derivatives are $p$-Convex %A Sevda Sezer %T Hermite-Hadamard Type Inequalities for the Functions Whose Absolute Values of First Derivatives are $p$-Convex %D 2021 %J Fundamental Journal of Mathematics and Applications %P 2645-8845- %V 4 %N 2 %R doi: 10.33401/fujma.881979 %U 10.33401/fujma.881979
ISNAD Sezer, Sevda . "Hermite-Hadamard Type Inequalities for the Functions Whose Absolute Values of First Derivatives are $p$-Convex". Fundamental Journal of Mathematics and Applications 4 / 2 (Haziran 2021): 88-99 . https://doi.org/10.33401/fujma.881979
AMA Sezer S. Hermite-Hadamard Type Inequalities for the Functions Whose Absolute Values of First Derivatives are $p$-Convex. FUJMA. 2021; 4(2): 88-99.
Vancouver Sezer S. Hermite-Hadamard Type Inequalities for the Functions Whose Absolute Values of First Derivatives are $p$-Convex. Fundamental Journal of Mathematics and Applications. 2021; 4(2): 88-99.
IEEE S. Sezer , "Hermite-Hadamard Type Inequalities for the Functions Whose Absolute Values of First Derivatives are $p$-Convex", Fundamental Journal of Mathematics and Applications, c. 4, sayı. 2, ss. 88-99, Haz. 2021, doi:10.33401/fujma.881979
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