scholarly journals New Quantum Estimates of Trapezium-Type Inequalities for Generalized ϕ-Convex Functions

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1047 ◽  
Author(s):  
Miguel J. Vivas-Cortez ◽  
Rozana Liko ◽  
Artion Kashuri ◽  
Jorge E. Hernández Hernández
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Type Inequality ◽  
Trapezium Type ◽  
New Class ◽  
Differentiable Functions ◽  
Special Cases

In this paper, a quantum trapezium-type inequality using a new class of function, the so-called generalized ϕ -convex function, is presented. A new quantum trapezium-type inequality for the product of two generalized ϕ -convex functions is provided. The authors also prove an identity for twice q - differentiable functions using Raina’s function. Utilizing the identity established, certain quantum estimated inequalities for the above class are developed. Various special cases have been studied. A brief conclusion is also given.

scholarly journals Some Hermite-Hadamard type inequalities for (P;m)-function and quasi m-convex functions

2020 ◽  
Vol 10 (1) ◽  
pp. 78-84
Author(s):  
Mahir Kadakal
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
New Class ◽  
Special Cases ◽  
First Time ◽  
Class Of Functions

In this paper, we introduce a new class of functions called as (P;m)-function and quasi-m-convex function. Some inequalities of Hadamard's type for these functions are given. Some special cases are discussed. Results represent signicant renement and improvement of the previous results. We should especially mention that the denition of (P;m)-function and quasi-m-convexity are given for the first time in the literature and moreover, the results obtained in special cases coincide with thewell-known results in the literature.

scholarly journals Some inequalities for strongly $(p,h)$-harmonic convex functions

2019 ◽  
Vol 11 (1) ◽  
pp. 119-135
Author(s):  
M.A. Noor ◽  
K.I. Noor ◽  
S. Iftikhar
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
New Class ◽  
Special Cases ◽  
Harmonic Convex

In this paper, we show that harmonic convex functions $f$ is strongly $(p, h)$-harmonic convex functions if and only if it can be decomposed as $g(x) = f(x) - c (\frac{1}{x^p})^2,$ where $g(x)$ is $(p, h)$-harmonic convex function. We obtain some new estimates  class of strongly $(p, h)$-harmonic convex functions involving hypergeometric and beta functions. As applications of our results, several important special cases are discussed. We also introduce a new class of harmonic convex functions, which is called strongly $(p, h)$-harmonic $\log$-convex functions. Some new Hermite-Hadamard type inequalities for strongly $(p, h)$-harmonic $log$-convex functions are obtained. These results  can be viewed as important refinement and significant improvements of the new and previous known results. The ideas and techniques of this paper may stimulate further research.

scholarly journals General Raina fractional integral inequalities on coordinates of convex functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Dumitru Baleanu ◽  
Artion Kashuri ◽  
Pshtiwan Othman Mohammed ◽  
Badreddine Meftah
Keyword(s):  
Mathematical Model ◽  
Fractional Calculus ◽  
Convex Function ◽  
Mathematical Analysis ◽  
Integral Inequality ◽  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Differentiable Functions ◽  
Special Cases

AbstractIntegral inequality is an interesting mathematical model due to its wide and significant applications in mathematical analysis and fractional calculus. In this study, authors have established some generalized Raina fractional integral inequalities using an $(l_{1},h_{1})$ ( l 1 , h 1 ) -$(l_{2},h_{2})$ ( l 2 , h 2 ) -convex function on coordinates. Also, we obtain an integral identity for partial differentiable functions. As an effect of this result, two interesting integral inequalities for the $(l_{1},h_{1})$ ( l 1 , h 1 ) -$(l_{2},h_{2})$ ( l 2 , h 2 ) -convex function on coordinates are given. Finally, we can say that our findings recapture some recent results as special cases.

Integral inequalities for differentiable p-harmonic convex functions

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6575-6584 ◽  
Author(s):  
Muhammad Noor ◽  
Khalida Noor ◽  
Sabah Iftikhar
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Integral Inequalities ◽  
Absolute Value ◽  
New Class ◽  
Special Cases ◽  
Harmonic Convex

In this paper, we consider a new class of harmonic convex functions, which is called p-harmonic convex function. Several new Hermite-Hadamard, midpoint, Trapezoidal and Simpson type inequalities for functions whose derivatives in absolute value are p-harmonic convex are obtained. Some special cases are discussed. The ideas and techniques of this paper may stimulate further research.

scholarly journals Trapezium-Type Inequalities for k -Fractional Integral via New Exponential-Type Convexity and Their Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Artion Kashuri ◽  
Sajid Iqbal ◽  
Saad Ihsan Butt ◽  
Jamshed Nasir ◽  
Kottakkaran Sooppy Nisar ◽  
...  
Keyword(s):  
Applied Sciences ◽  
Convex Function ◽  
Error Estimates ◽  
Exponential Type ◽  
Convex Functions ◽  
Fractional Integral ◽  
Type Inequality ◽  
Trapezium Type ◽  
Special Means ◽  
Algebraic Properties

In this paper, the authors investigated the concept of s , m -exponential-type convex functions and their algebraic properties. New generalizations of Hermite–Hadamard-type inequality for the s , m -exponential-type convex function ψ and for the products of two s , m -exponential-type convex functions ψ and ϕ are proved. Many refinements of the (H–H) inequality via s , m -exponential-type convex are obtained. Finally, several new bounds for special means and new error estimates for the trapezoidal and midpoint formula are provided as well. The ideas and techniques of this paper may stimulate further research in different areas of pure and applied sciences.

scholarly journals On approximately harmonic h-convex functions depending on a given function

Filomat ◽  
2019 ◽  
Vol 33 (12) ◽  
pp. 3783-3793 ◽  
Author(s):  
Muhammad Awan ◽  
Muhammad Noor ◽  
Marcela Mihai ◽  
Khalida Noor ◽  
Nousheen Akhtar
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Integral Inequalities ◽  
New Class ◽  
Special Cases ◽  
Harmonic Convex ◽  
Harmonic Convexity

A new class of harmonic convex function depending on given functions which is called as ?approximately harmonic h-convex functions? is introduced. With the discussion of special cases it is shown that this class unifies other classes of approximately harmonic h-convex function. Some associated integral inequalities with these new classes of harmonic convexity are also obtained. Several special cases of the main results are also discussed.

scholarly journals A note on generalized convex functions

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Syed Zaheer Ullah ◽  
Muhammad Adil Khan ◽  
Yu-Ming Chu
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Type Inequality ◽  
Generalized Convex Functions

Abstract In the article, we provide an example for a η-convex function defined on rectangle is not convex, prove that every η-convex function defined on rectangle is coordinate η-convex and its converse is not true in general, define the coordinate $(\eta _{1}, \eta _{2})$(η1,η2)-convex function and establish its Hermite–Hadamard type inequality.

scholarly journals New Modifications of Integral Inequalities via ℘-Convexity Pertaining to Fractional Calculus and Their Applications

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1753
Author(s):  
Saima Rashid ◽  
Aasma Khalid ◽  
Omar Bazighifan ◽  
Georgia Irina Oros
Keyword(s):  
Integral Operator ◽  
Convex Functions ◽  
Hypergeometric Functions ◽  
Fractional Integral ◽  
Type Inequality ◽  
Fractional Integral Operator ◽  
Integral Inequalities ◽  
Convex Mappings ◽  
Special Cases ◽  
Harmonically Convex Functions

Integral inequalities for ℘-convex functions are established by using a generalised fractional integral operator based on Raina’s function. Hermite–Hadamard type inequality is presented for ℘-convex functions via generalised fractional integral operator. A novel parameterized auxiliary identity involving generalised fractional integral is proposed for differentiable mappings. By using auxiliary identity, we derive several Ostrowski type inequalities for functions whose absolute values are ℘-convex mappings. It is presented that the obtained outcomes exhibit classical convex and harmonically convex functions which have been verified using Riemann–Liouville fractional integral. Several generalisations and special cases are carried out to verify the robustness and efficiency of the suggested scheme in matrices and Fox–Wright generalised hypergeometric functions.

scholarly journals Simpson type inequalities and applications

2021 ◽  
Author(s):  
Muhammad Uzair Awan ◽  
Muhammad Zakria Javed ◽  
Michael Th. Rassias ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor
Keyword(s):  
Quadrature Formula ◽  
Convex Functions ◽  
Integral Identity ◽  
Higher Order ◽  
Auxiliary Result ◽  
First Order ◽  
New Class ◽  
Differentiable Functions

AbstractA new generalized integral identity involving first order differentiable functions is obtained. Using this identity as an auxiliary result, we then obtain some new refinements of Simpson type inequalities using a new class called as strongly (s, m)-convex functions of higher order of $$\sigma >0$$ σ > 0 . We also discuss some interesting applications of the obtained results in the theory of means. In last we present applications of the obtained results in obtaining Simpson-like quadrature formula.

scholarly journals On Sherman-Steffensen type inequalities

Filomat ◽  
2018 ◽  
Vol 32 (13) ◽  
pp. 4627-4638 ◽  
Author(s):  
Marek Niezgoda
Keyword(s):  
Convex Functions ◽  
Type Inequality ◽  
Special Cases ◽  
Steffensen Inequality

In this work, Sherman-Steffensen type inequalities for convex functions with not necessarily non-negative coefficients are established by using Steffensen?s conditions. The Brunk, Bellman and Olkin type inequalities are derived as special cases of the Sherman-Steffensen inequality. The superadditivity of the Jensen-Steffensen functional is investigated via Steffensen?s condition for the sequence of the total sums of all entries of the involved vectors of coeffecients. Some results of Baric et al. [2] and of Krnic et al. [11] on the monotonicity of the functional are recovered. Finally, a Sherman-Steffensen type inequality is shown for a row graded matrix.

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