Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2021, Cilt: 70 Sayı: 2, 1011 - 1035, 31.12.2021
https://doi.org/10.31801/cfsuasmas.848853

Öz

Kaynakça

  • Butt, S. I., Nadeem, M., Qaisar, S., Akdemir, A. O., Abdeljawad, T., Hermite-Jensen-Mercer type inequalities for conformable integrals and related results, Adv. Differ. Equ., 1 (2020), 1–24. https://doi.org/10.1186/s13662-020-02968-4
  • Chu, H. H., Kalsoom, H., Rashid, S., Idrees, M., Safdar, F., Chu, Y-M., Baleanu, D., Quantum analogs of Ostrowski type inequalities for Rainas function correlated with coordinated generalized η–convex functions, Symmetry, 12(2) (2020), 1–26. https://doi.org/10.3390/sym12020308
  • Dragomir, S. S., Fitzpatrik, S., The Hadamard’s inequality for s–convex functions in the second sense, Demonstratio Math., 32(4) (1999), 687-696. https://doi.org/10.1515/dema-1999-0403
  • Eftekhari, N., Some remarks on (s,m)–convexity in the second sense, J. Math. Inequal., 8 (2014), 489-495. dx.doi.org/10.7153/jmi-08-36
  • Fejer, L., Über die Fourierreihen, II. Math. Naturwiss. Anz Ungar. Akad. Wiss., 24 (1906).
  • Hadamard, J., Etude sur les proprietes des fonctions entieres en particulier d’une fonction consideree par Riemann, J. Math. Pures. Appl., 58 (1893), 171–215. http://eudml.org/doc/234668
  • Hernandez, H., Jorge, E., Vivas–Cortez, M., Hermite–Hadamard inequalities type for Raina’s Fractional integral operator using η–convex functions, Revista de Mathematica Teoriay Aplicaciones., 26(1) (2019), 1–20. http://dx.doi.org/10.15517/rmta.v26i1.35515
  • Khan, S., Khan, M. A., Butt, S. I., Chu, Y-M., A new bound for the Jensen gap pertaining twice differentiable functions with applications, Adv. Differ. Equ., 1 (2020), 1–11. https://doi.org/10.1186/s13662-020-02794-8
  • Mehmood, N., Butt, S. I., Pecaric, D., Pecaric, J., Generalizations of cyclic refinements of Jensena’s inequality by Lidstonea’s polynomial with applications in Information Theory, J. Math. Inequal., 14(1) (2020), 249–271. dx.doi.org/10.7153/jmi-2020-14-17
  • Niculescu, C. P., Persson, L. E., Convex Functions and Their Applications, Springer, New York, 2006. https://doi.org/10.1007/0-387-31077-0
  • Özdemir, M. E., Yildiz, C., Akdemir, A. O., Set, E., On some inequalities for s–convex functions and applications, J. Ineq. Appl., 333 (2013), 2–11. https://doi.org/10.1186/1029-242X-2013-333
  • Raina, R. K., On generalized Wright’s hypergeometric functions and fractional calculus operators, East Asian Math. J., 21(2) (2005), 191–203.
  • Sarikaya, M. Z., Saglam, A., Yildirim, H., On some Hadamard type inequalities for h–convex functions, J. Math. Anal., 2(3) (2008), 335–341. https://doi.org/10.1186/s13660-019-2151-2
  • Set, E., Noor, M. A., Awan, M. U., Gözpinar, A., Generalized Hermite–Hadamard type inequalities involving fractional integral operator, J. Inequal. Appl., 169 (2017), 1–10. https://doi.org/10.1186/s13660-017-1444-6
  • Set, E., Some new generalizations of Ostrowski type inequalities for s-convex functions via fractional integral operators, Filomat., 32(16) (2018), 5595–5609. https://doi.org/10.2298/FIL1816595S
  • Toader, G., Some generalizations of the convexity, Proceedings of The Colloquium on Approximation and Optimization, Univ. Cluj–Napoca, Cluj–Napoca, (1985), 329–338.
  • Xi, B. Y., Q, F., Some integral inequalities of Hermite–Hadamard type for convex functions with applications to means, J. Funct. Spaces. Appl., 2012 Article ID 980438, (2012), 1–14. https://doi.org/10.1155/2012/980438
  • Butt, S. I., Tariq, M., Aslam, A., Ahmad, H., Nofal, T. A., Hermite-Hadamard type inequalities via generalized harmonic exponential convexity and applications, Journal of Function Spaces, 2021 Article ID 5533491 (2021), 12 pages. https://doi.org/10.1155/2021/5533491
  • Butt, S. I., Kashuri, A., Tariq, M., Nasir, J., Aslam, A., Gao, W., n-polynomial exponential type p-convex function with some related inequalities and their applications, Heliyon, 6(11) (2020), e05420 ISSN 2405-8440. https://doi.org/10.1016/j.heliyon.2020.e05420
  • Butt, S. I., Kashuri, A., Tariq, M., Nasir, J., Aslam, A., Gao, W., Hermite-Hadamard-type inequalities via n-polynomial exponential-type convexity and their applications, Adv. Differ. Equ., 508 (2020). https://doi.org/10.1186/s13662-020-02967-5
  • Gao, W., Kashuri, A., Butt, S. I., Tariq, M., Aslam, A., Nadeem, M., New inequalities via n-polynomial harmonically exponential type convex functions, AIMS Mathematics, 5(6) (2020), 6856-6873. doi: 10.3934/math.2020440
  • Butt, S. I., Kashuri, A., Umar, M., Aslam, A., Gao, W., Hermite-Jensen-Mercer type inequalities via ψ-Riemann-Liouville k-fractional integrals, AIMS Mathematics, 5(5) (2020), 5193-5220. doi:10.3934/math.2020334

New integral type inequalities via Raina-convex functions and its applications

Yıl 2021, Cilt: 70 Sayı: 2, 1011 - 1035, 31.12.2021
https://doi.org/10.31801/cfsuasmas.848853

Öz

In this work, we discuss and introduce the novel literature about Raina-convex function and its algebraic properties. In addition, We elaborate and investigate Hermite-Hadamard and Fejer-type inequalities for newly discussed definition. Finally, using newly introduced definition, we find and prove amazing new integral type inequalities and applications for mean to positive real numbers. The amazing techniques and wonderful ideas of this paper may inspire and motivate for further activities and research in this direction furthermore.

Kaynakça

  • Butt, S. I., Nadeem, M., Qaisar, S., Akdemir, A. O., Abdeljawad, T., Hermite-Jensen-Mercer type inequalities for conformable integrals and related results, Adv. Differ. Equ., 1 (2020), 1–24. https://doi.org/10.1186/s13662-020-02968-4
  • Chu, H. H., Kalsoom, H., Rashid, S., Idrees, M., Safdar, F., Chu, Y-M., Baleanu, D., Quantum analogs of Ostrowski type inequalities for Rainas function correlated with coordinated generalized η–convex functions, Symmetry, 12(2) (2020), 1–26. https://doi.org/10.3390/sym12020308
  • Dragomir, S. S., Fitzpatrik, S., The Hadamard’s inequality for s–convex functions in the second sense, Demonstratio Math., 32(4) (1999), 687-696. https://doi.org/10.1515/dema-1999-0403
  • Eftekhari, N., Some remarks on (s,m)–convexity in the second sense, J. Math. Inequal., 8 (2014), 489-495. dx.doi.org/10.7153/jmi-08-36
  • Fejer, L., Über die Fourierreihen, II. Math. Naturwiss. Anz Ungar. Akad. Wiss., 24 (1906).
  • Hadamard, J., Etude sur les proprietes des fonctions entieres en particulier d’une fonction consideree par Riemann, J. Math. Pures. Appl., 58 (1893), 171–215. http://eudml.org/doc/234668
  • Hernandez, H., Jorge, E., Vivas–Cortez, M., Hermite–Hadamard inequalities type for Raina’s Fractional integral operator using η–convex functions, Revista de Mathematica Teoriay Aplicaciones., 26(1) (2019), 1–20. http://dx.doi.org/10.15517/rmta.v26i1.35515
  • Khan, S., Khan, M. A., Butt, S. I., Chu, Y-M., A new bound for the Jensen gap pertaining twice differentiable functions with applications, Adv. Differ. Equ., 1 (2020), 1–11. https://doi.org/10.1186/s13662-020-02794-8
  • Mehmood, N., Butt, S. I., Pecaric, D., Pecaric, J., Generalizations of cyclic refinements of Jensena’s inequality by Lidstonea’s polynomial with applications in Information Theory, J. Math. Inequal., 14(1) (2020), 249–271. dx.doi.org/10.7153/jmi-2020-14-17
  • Niculescu, C. P., Persson, L. E., Convex Functions and Their Applications, Springer, New York, 2006. https://doi.org/10.1007/0-387-31077-0
  • Özdemir, M. E., Yildiz, C., Akdemir, A. O., Set, E., On some inequalities for s–convex functions and applications, J. Ineq. Appl., 333 (2013), 2–11. https://doi.org/10.1186/1029-242X-2013-333
  • Raina, R. K., On generalized Wright’s hypergeometric functions and fractional calculus operators, East Asian Math. J., 21(2) (2005), 191–203.
  • Sarikaya, M. Z., Saglam, A., Yildirim, H., On some Hadamard type inequalities for h–convex functions, J. Math. Anal., 2(3) (2008), 335–341. https://doi.org/10.1186/s13660-019-2151-2
  • Set, E., Noor, M. A., Awan, M. U., Gözpinar, A., Generalized Hermite–Hadamard type inequalities involving fractional integral operator, J. Inequal. Appl., 169 (2017), 1–10. https://doi.org/10.1186/s13660-017-1444-6
  • Set, E., Some new generalizations of Ostrowski type inequalities for s-convex functions via fractional integral operators, Filomat., 32(16) (2018), 5595–5609. https://doi.org/10.2298/FIL1816595S
  • Toader, G., Some generalizations of the convexity, Proceedings of The Colloquium on Approximation and Optimization, Univ. Cluj–Napoca, Cluj–Napoca, (1985), 329–338.
  • Xi, B. Y., Q, F., Some integral inequalities of Hermite–Hadamard type for convex functions with applications to means, J. Funct. Spaces. Appl., 2012 Article ID 980438, (2012), 1–14. https://doi.org/10.1155/2012/980438
  • Butt, S. I., Tariq, M., Aslam, A., Ahmad, H., Nofal, T. A., Hermite-Hadamard type inequalities via generalized harmonic exponential convexity and applications, Journal of Function Spaces, 2021 Article ID 5533491 (2021), 12 pages. https://doi.org/10.1155/2021/5533491
  • Butt, S. I., Kashuri, A., Tariq, M., Nasir, J., Aslam, A., Gao, W., n-polynomial exponential type p-convex function with some related inequalities and their applications, Heliyon, 6(11) (2020), e05420 ISSN 2405-8440. https://doi.org/10.1016/j.heliyon.2020.e05420
  • Butt, S. I., Kashuri, A., Tariq, M., Nasir, J., Aslam, A., Gao, W., Hermite-Hadamard-type inequalities via n-polynomial exponential-type convexity and their applications, Adv. Differ. Equ., 508 (2020). https://doi.org/10.1186/s13662-020-02967-5
  • Gao, W., Kashuri, A., Butt, S. I., Tariq, M., Aslam, A., Nadeem, M., New inequalities via n-polynomial harmonically exponential type convex functions, AIMS Mathematics, 5(6) (2020), 6856-6873. doi: 10.3934/math.2020440
  • Butt, S. I., Kashuri, A., Umar, M., Aslam, A., Gao, W., Hermite-Jensen-Mercer type inequalities via ψ-Riemann-Liouville k-fractional integrals, AIMS Mathematics, 5(5) (2020), 5193-5220. doi:10.3934/math.2020334
Toplam 22 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Saad Ihsan Butt 0000-0001-7192-8269

Muhammad Nadeem Bu kişi benim 0000-0003-2714-4314

Muhammad Tariq Bu kişi benim 0000-0002-2078-0652

Adnan Aslam 0000-0003-4523-8023

Yayımlanma Tarihi 31 Aralık 2021
Gönderilme Tarihi 28 Aralık 2020
Kabul Tarihi 7 Haziran 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 70 Sayı: 2

Kaynak Göster

APA Butt, S. I., Nadeem, M., Tariq, M., Aslam, A. (2021). New integral type inequalities via Raina-convex functions and its applications. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 70(2), 1011-1035. https://doi.org/10.31801/cfsuasmas.848853
AMA Butt SI, Nadeem M, Tariq M, Aslam A. New integral type inequalities via Raina-convex functions and its applications. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Aralık 2021;70(2):1011-1035. doi:10.31801/cfsuasmas.848853
Chicago Butt, Saad Ihsan, Muhammad Nadeem, Muhammad Tariq, ve Adnan Aslam. “New Integral Type Inequalities via Raina-Convex Functions and Its Applications”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70, sy. 2 (Aralık 2021): 1011-35. https://doi.org/10.31801/cfsuasmas.848853.
EndNote Butt SI, Nadeem M, Tariq M, Aslam A (01 Aralık 2021) New integral type inequalities via Raina-convex functions and its applications. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70 2 1011–1035.
IEEE S. I. Butt, M. Nadeem, M. Tariq, ve A. Aslam, “New integral type inequalities via Raina-convex functions and its applications”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 70, sy. 2, ss. 1011–1035, 2021, doi: 10.31801/cfsuasmas.848853.
ISNAD Butt, Saad Ihsan vd. “New Integral Type Inequalities via Raina-Convex Functions and Its Applications”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70/2 (Aralık 2021), 1011-1035. https://doi.org/10.31801/cfsuasmas.848853.
JAMA Butt SI, Nadeem M, Tariq M, Aslam A. New integral type inequalities via Raina-convex functions and its applications. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70:1011–1035.
MLA Butt, Saad Ihsan vd. “New Integral Type Inequalities via Raina-Convex Functions and Its Applications”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 70, sy. 2, 2021, ss. 1011-35, doi:10.31801/cfsuasmas.848853.
Vancouver Butt SI, Nadeem M, Tariq M, Aslam A. New integral type inequalities via Raina-convex functions and its applications. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70(2):1011-35.

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