• Title, Summary, Keyword: convex functions

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NEW INEQUALITIES FOR GENERALIZED LOG h-CONVEX FUNCTIONS

  • NOOR, MUHAMMAD ASLAM;NOOR, KHALIDA INAYAT;SAFDAR, FARHAT
    • Journal of applied mathematics & informatics
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    • v.36 no.3_4
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    • pp.245-256
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    • 2018
  • In the paper, we introduce some new classes of generalized logh-convex functions in the first sense and in the second sense. We establish Hermite-Hadamard type inequality for different classes of generalized convex functions. It is shown that the classes of generalized log h-convex functions in both senses include several new and known classes of log h convex functions. Several special cases are also discussed. Results proved in this paper can be viewed as a new contributions in this area of research.

ON SOME NEW FRACTIONAL HERMITE-HADAMARD TYPE INEQUALITIES FOR CONVEX AND CO-ORDINATED CONVEX FUNCTIONS

  • Ali, Muhammad Aamir;Budak, Huseyin;Sakhi, Sadia
    • Korean Journal of Mathematics
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    • v.28 no.4
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    • pp.955-971
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    • 2020
  • In this study, some new inequalities of Hermite-Hadamard type for convex and co-ordinated convex functions via Riemann-Liouville fractional integrals are derived. It is also shown that the results obtained in this paper are the extension of some earlier ones.

Certain Subclasses of k-Uniformly Starlike and Convex Functions of Order α and Type β with Varying Argument Coefficients

  • AOUF, MOHAMED KAMAL;MAGESH, NANJUNDAN;YAMINI, JAGADESAN
    • Kyungpook Mathematical Journal
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    • v.55 no.2
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    • pp.383-394
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    • 2015
  • In this paper, we define two new subclass of k-uniformly starlike and convex functions of order ${\alpha}$ type ${\beta}$ with varying argument of coefficients. Further, we obtain coefficient estimates, extreme points, growth and distortion bounds, radii of starlikeness, convexity and results on modified Hadamard products.

ON TRIGONOMETRICALLY QUASI-CONVEX FUNCTIONS

  • Numan, Selim;Iscan, Imdat
    • Honam Mathematical Journal
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    • v.43 no.1
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    • pp.130-140
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    • 2021
  • In this paper, we introduce and study the concept of trigonometrically quasi-convex function. We prove Hermite-Hadamard type inequalities for the newly introduced class of functions and obtain some new Hermite-Hadamard inequalities for functions whose first derivative in absolute value, raised to a certain power which is greater than one, respectively at least one, is trigonometrically quasi-convex convex. We also extend our initial results to functions of several variables. Next, we point out some applications of our results to give estimates for the approximation error of the integral the function in the trapezoidal formula.