İlgi alanları

• MakaleAçık Erişim2025/r/bayburt/14138
  EARTHQUAKE -FUNCTIONS WITH SOME RELATED INEQUALITIES AND THEIR APPLICATIONS

  Özcan, Serap; Kadakal, Mahir; Iscan, Imdat; Kadakal, Huriye

  As researchers, our primary commitment is to engage in the creation of scientific and academic knowledge. Recognizing the importance of societal impact, we also strive to contribute to social awareness through our work. Natural disasters, such as floods, earthquakes, avalanches, landslides, tsunamis, and others, frequently afflict regions globally, resulting in profound human losses and extensive material damage. Notably, the earthquake that struck our country on February 6, 2023, marked as the disaster of the century, deeply affected eleven provinces, leading to a tragic loss of tens of thousands of lives. In this paper, we investigate the concept of earthquake P-functions. We establish the Hermite-Hadamard inequality for this class of functions and derive several refinements of the Hermite-Hadamard type inequality for functions whose first derivative, in absolute value, at a certain power, is an earthquake P-function. We present some applications of the trapezoidal formula. We also provide new bounds for special means of different non-negative real numbers.

  İncele
• MakaleAçık Erişim2025Scopus SJRQ3/r/bayburt/12943
  INVERSE TRIGONOMETRICALLY CONVEXITY AND BETTER APPROXIMATIONS

  Kadakal, Huriye; Kadakal, Mahir

  In this paper, we introduce and study the concept of inverse trigonometrically convex functions and their some algebraic properties. We prove some Hermite-Hadamard type integral 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 is inverse trigonometrically convex. Moreover, we proved that Hölder-İşcan and improved power-mean integral inequalities give a better approach than Hölder and power-mean inequalities.

  İncele
• MakaleAçık Erişim2025Scopus SJRQ2/r/bayburt/12815
  Some new Simpson type integral inequalities for (s, P)-functions

  Kadakal, M.; İşcan, İ.; Kadakal, H.

  In this paper, we establish some new Simpson type inequalities for functions, whose first deriva-tive in absolute value is (s, P)-function by using Hölder, power-mean and Hölder-İşcan inequalities. After that, we compare the results obtained with both Hölder, Hölder-İşcan integral inequalities and prove that the Hölder-İşcan integral inequality gives a better approximation, than the Hölder inequality. Also, some applications to special means of real numbers are also given.

  İncele
• MakaleYalnız künye2025Scopus SJRQ2/r/bayburt/12748
  HERMITE–HADAMARD TYPE INTEGRAL INEQUALITIES FOR SEMIHARMONICALLY P-FUNCTIONS

  Kadakal, Mahir; Iscan, İMDAT; Kadakal, Huriye

  The authors introduce the concept of semiharmonically P-functions and establish some Hermite–Hadamard type integral inequalities for these classes of functions. Also, the authors compare the results obtained Hölder and Hölder–˙ I¸scan inequalities and show that the result obtained with Hölder–˙ I¸scan inequalities give better approach than the others. Some applications to special means of real numbers are also given.

  İncele
• MakaleAçık Erişim2024/r/bayburt/14115
  GENERALIZED n-POLYNOMIAL P- FUNCTIONS WITH SOME RELATED INEQUALITIES AND THEIR APPLICATIONS

  Ozcan, Serap; Kadakal, Mahir; Iscan, Imdat; Kadakal, Huriye

  In this paper, we introduce the notion of generalized n-polynomial Pfunction. We explore some algebraic properties of this function class. Additionally, we establish a new trapezium type inequality for this generalized class of functions and derive several refinements of the trapezium type inequality for functions whose first derivative in absolute value at a certain power is generalized n-polynomial P-function. Finally, we conclude our paper by exploring some applications of the results we have obtained in the context of special means. Our novel findings generalize previously known results in the literature.

  AtıfWoS1·OpenAlex1

  İncele
• MakaleAçık Erişim2024Scopus SJRQ4/r/bayburt/13100
  Better approximations for quasi-convex functions

  Kadakal, Huriye

  In this paper, by using Hölder-Işcan, Hölder integral inequality and an general identity for diérentiable functions we can get new estimates on generalization of Hadamard, Ostrowski and Simpson type integral inequalities for functions whose derivatives in absolute value at certain power are quasi-convex functions. It is proved that the result obtained Hölder-Işcan integral inequality is better than the result obtained Hölder inequality.

  AtıfScopus1·WoS1

  İncele
• MakaleAçık Erişim2024Scopus SJRQ4/r/bayburt/13040
  Some Hermite-Hadamard type integral inequalities for functions whose first derivatives are trigonometrically ρ-convex

  Kadakal, Huriye; Kadakal, Mahir

  In this manuscript, we obtain refinements of the Hermite-Hadamard type inequalites for functions whose first derivative in absolute value, raised to a certain power which is greater than one, respectively at least one, is trigonometrically ρ-convex. We also show that our results coincide with previous results.

  AtıfScopus3·OpenAlex1

  İncele
• MakaleAçık Erişim2024Scopus SJRQ3/r/bayburt/12970
  Some New Integral Inequalities for Exponential Type P-functions

  Kadakal, Mahir; İmdat, Işcan; Kadakal, Huriye

  In this paper, by using an identity we obtain some new Hermite-Hadamard type inequalities for functions whose first derivative in absolute value is exponential type P-function by using Hölder and power-mean integral inequalities. Then, the authors compare the results obtained with both Hölder, Hölder-İşcan integral inequalities and prove that the Hölder-İşcan integral inequality gives a better approximation than the Hölder integral inequality. Also, some applications to special means of real numbers are also given.

  AtıfScopus1·WoS2

  İncele
• MakaleYalnız künye2024Scopus SJRQ4/r/bayburt/11901
  Earthquake convexity and some new related inequalities

  Kadakal, Mahir; Işcan, Imdat; Kadakal, Huriye

  Unfortunately, eleven of our provinces were severely affected due to two severe earthquakes that occurred in our country, the Republic of Turkey, on February 6, 2023. As a result, thousands of buildings were destroyed and tens of thousands of our citizens lost their lives. From past to present, such disasters have occurred in many parts of our world and will continue to happen. In order to raise awareness for researchers and academicians reading our article, we will give a new definition of convexity in this article, and we will call it "earthquake convexity". In this paper, we study some algebraic properties of the earthquake convexity. Then we compare the results obtained with both Hölder, Hölder-Işcan inequalities and power-mean, improved power-mean integral inequalities and show that the results obtained with Hölder-Işcan and improved power-mean inequalities are better than the others. Some applications to special means of real numbers are also given.

  AtıfWoS1·OpenAlex3

  İncele
• MakaleYayıncıda açık erişim2024Scopus SJRQ2/r/bayburt/11876
  Generalized strongly n-polynomial convex functions and related inequalities

  Özcan, Serap; Kadakal, Mahir; İşcan, İmdat; Kadakal, Huriye

  This paper focuses on introducing and examining the class of generalized strongly n-polynomial convex functions. Relationships between these functions and other types of convex functions are explored. The Hermite–Hadamard inequality is established for generalized strongly n-polynomial convex functions. Additionally, new integral inequalities of Hermite–Hadamard type are derived for this class of functions using the Hölder–İşcan integral inequality. The results obtained in this paper are compared with those known in the literature, demonstrating the superiority of the new results. Finally, some applications for special means are provided.

  AtıfScopus5·WoS5·OpenAlex6

  İncele