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AIMS Mathematics

2020, Volume 5, Issue 4: 3525-3546. doi: 10.3934/math.2020229
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Research article

New weighted generalizations for differentiable exponentially convex mapping with application

  • 1.
    Department of Mathematics, Government College (GC) University, Faisalabad, Pakistan
  • 2.
    Abdus Salam School of Mathematical Sciences, Government College (GC) University Lahore, Lahore, Pakistan
  • 3.
    Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan
  • 4.
    Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China
  • 5.
    School of Mathematics and Statistics, Changsha University of Science & Technology, Changsha 413000, P. R. China
  • Received: 19 December 2019 Accepted: 25 March 2020 Published: 10 April 2020

  • MSC : 26D10, 26D15, 26E60

  • The main aim of the present paper is to present a novel approach base on the exponentially convex function to broaden the utilization of celebrated Hermite-Hadamard type inequality. The proposed technique presents an auxiliary result of constructing the set of base functions and gives deformation equations in a simple form. The auxiliary result in the convexity has provided a convenient way of establishing the convergence region of several novel results. The strategy is not limited to the small parameter, such as in the classical method. The numerical examples obtained by the proposed approach indicate that the approach is easy to implement and computationally very attractive. The implementation of this numerical scheme clearly exhibits its effectiveness, reliability, and easiness regarding the applications in error estimates for weighted mean, the integral formula, $r$th moments of a continuous random variable, application to weighted special means and in developing the variants by extraordinary choices of $n$ and $\theta$ as well as its better approximation.

    Citation: Saima Rashid, Rehana Ashraf, Muhammad Aslam Noor, Khalida Inayat Noor, Yu-Ming Chu. New weighted generalizations for differentiable exponentially convex mapping with application[J]. AIMS Mathematics, 2020, 5(4): 3525-3546. doi: 10.3934/math.2020229

    Related Papers:

  • The main aim of the present paper is to present a novel approach base on the exponentially convex function to broaden the utilization of celebrated Hermite-Hadamard type inequality. The proposed technique presents an auxiliary result of constructing the set of base functions and gives deformation equations in a simple form. The auxiliary result in the convexity has provided a convenient way of establishing the convergence region of several novel results. The strategy is not limited to the small parameter, such as in the classical method. The numerical examples obtained by the proposed approach indicate that the approach is easy to implement and computationally very attractive. The implementation of this numerical scheme clearly exhibits its effectiveness, reliability, and easiness regarding the applications in error estimates for weighted mean, the integral formula, $r$th moments of a continuous random variable, application to weighted special means and in developing the variants by extraordinary choices of $n$ and $\theta$ as well as its better approximation.


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