scholarly journals Hermite–Hadamard-Type Inequalities for the Generalized Geometrically Strongly Modified h -Convex Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Xishan Yu ◽  
Muhammad Shoaib Saleem ◽  
Shumaila Waheed ◽  
Ilyas Khan
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Applied Mathematics ◽  
Optimization Theory ◽  
New Class ◽  
Convexity Theory ◽  
Class Of Functions

Convexity theory becomes a hot area of research due to its applications in pure and applied mathematics, especially in optimization theory. The aim of this paper is to introduce a broader class of convex functions by unifying geometrically strong convex function with h convex functions. This new class of functions is called as generalized geometrically strongly modified h -convex functions. We established Hermite–Hadamard-type inequalities for the generalized geometrically strongly modified h -convex functions. Our results can be considered as generalization and extension of literature.

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 of Generalized p-Convex Functions concerning Raina’s Fractional Integral Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Changyue Chen ◽  
Muhammad Shoaib Sallem ◽  
Muhammad Sajid Zahoor
Keyword(s):  
Integral Operator ◽  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Applied Mathematics ◽  
Optimization Theory ◽  
Integral Operators ◽  
Fractional Integral Operator ◽  
Fractional Integral Operators

Convex functions play an important role in pure and applied mathematics specially in optimization theory. In this paper, we will deal with well-known class of convex functions named as generalized p-convex functions. We develop Hermite–Hadamard-type inequalities for this class of convex function via Raina’s fractional integral operator.

scholarly journals New Inequalities for Strongly r-Convex Functions

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Huriye Kadakal
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Integral Identity ◽  
Integral Inequalities ◽  
Special Cases ◽  
Class Of Functions ◽  
New Inequalities

In this study, firstly we introduce a new concept called “strongly r-convex function.” After that we establish Hermite-Hadamard-like inequalities for this class of functions. Moreover, by using an integral identity together with some well known integral inequalities, we establish several new inequalities for n-times differentiable strongly r-convex functions. In special cases, the results obtained coincide with the well-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 Sandwich theorem for reciprocally strongly convex functions

2018 ◽  
Vol 52 (2) ◽  
pp. 171-184
Author(s):  
Mireya Bracamonte ◽  
José Giménez ◽  
Jesús Medina
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Stability Result ◽  
Real Interval ◽  
Strongly Convex Functions ◽  
Strongly Convex Function ◽  
Strongly Convex ◽  
Sandwich Theorem ◽  
Approximate Convexity ◽  
Class Of Functions

We introduce the notion of reciprocally strongly convex functions and we present some examples and properties of them. We also prove that two real functions f and g, defined on a real interval [a, b], satisfy for all x, y ∈ [a, b] and t ∈ [0, 1] iff there exists a reciprocally strongly convex function h : [a, b] → R such that f (x) ≤ h(x) ≤ g(x) for all x ∈ [a, b]. Finally, we obtain an approximate convexity result for reciprocally strongly convex functions; namely we prove a stability result of Hyers-Ulam type for this class of functions.

scholarly journals On Caputo–Fabrizio Fractional Integral Inequalities of Hermite–Hadamard Type for Modified h -Convex Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Xiaobin Wang ◽  
Muhammad Shoaib Saleem ◽  
Kiran Naseem Aslam ◽  
Xingxing Wu ◽  
Tong Zhou
Keyword(s):  
Integral Operator ◽  
Fractional Calculus ◽  
Convex Function ◽  
Convex Functions ◽  
Fractional Derivatives ◽  
Fractional Integral ◽  
Applied Mathematics ◽  
Fractional Integral Operator ◽  
Real Numbers ◽  
Special Means

The theory of convex functions plays an important role in engineering and applied mathematics. The Caputo–Fabrizio fractional derivatives are one of the important notions of fractional calculus. The aim of this paper is to present some properties of Caputo–Fabrizio fractional integral operator in the setting of h -convex function. We present some new Caputo–Fabrizio fractional estimates from Hermite–Hadamard-type inequalities. The results of this paper can be considered as the generalization and extension of many existing results of inequalities and convex functions. Moreover, we also present some application of our results to special means of real numbers.

Exponential trigonometric convex functions and Hermite-Hadamard type inequalities

2021 ◽  
Vol 71 (1) ◽  
pp. 43-56
Author(s):  
Mahir Kadakal ◽  
İmdat İşcan ◽  
Praveen Agarwal ◽  
Mohamed Jleli
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Integral Inequalities ◽  
Power Mean ◽  
Hadamard Inequality ◽  
Absolute Value ◽  
First Derivative ◽  
Algebraic Properties ◽  
Class Of Functions

Abstract In this manuscript, we introduce and study the concept of exponential trigonometric convex functions and their some algebraic properties. We obtain Hermite-Hadamard type 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, raised to a certain power which is greater than one, respectively at least one, is exponential trigonometric convex function. It has been shown that the result obtained with Hölder-İşcan and improved power-mean integral inequalities give better approximations than that obtained with Hölder and improved power-mean integral inequalities.

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 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 On HT-convexity and Hadamard-type inequalities

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shu-Ping Bai ◽  
Shu-Hong Wang ◽  
Feng Qi
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Arithmetic Mean ◽  
Logarithmic Mean ◽  
New Class

AbstractIn the paper, the authors define a new notion of “HT-convex function”, present some Hadamard-type inequalities for the new class of HT-convex functions and for the product of any two HT-convex functions, and derive some inequalities for the arithmetic mean and the p-logarithmic mean. These results generalize corresponding ones for HA-convex functions and MT-convex functions.

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