scholarly journals On Harmonically(p,h,m)-Preinvex Functions

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Shan-He Wu ◽  
Imran Abbas Baloch ◽  
İmdat İşcan
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Special Cases ◽  
Preinvex Functions

We define a new generalized class of harmonically preinvex functions named harmonically(p,h,m)-preinvex functions, which includes harmonic(p,h)-preinvex functions, harmonicp-preinvex functions, harmonich-preinvex functions, andm-convex functions as special cases. We also investigate the properties and characterizations of harmonically(p,h,m)-preinvex functions. Finally, we establish some integral inequalities to show the applications of harmonically(p,h,m)-preinvex functions.

scholarly journals Some Integral Inequalities for n -Polynomial ζ -Preinvex Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Shanhe Wu ◽  
Muhammad Uzair Awan ◽  
Muhammad Ubaid Ullah ◽  
Sadia Talib ◽  
Artion Kashuri
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Special Means ◽  
Special Cases ◽  
Preinvex Functions

In this paper, we study the properties of n -polynomial ζ -preinvex functions and establish some integral inequalities of Hermite-Hadamard type via this class of convex functions. Moreover, we discuss some special cases which provide a significant complement to the integral estimations of preinvex functions. Applications of the obtained results to the inequalities for special means are also considered.

scholarly journals On exponentially ϱ-preinvex functions and associated trapezium like inequalities

2021 ◽  
pp. 25-25
Author(s):  
Artion Kashuri ◽  
Muhammad Awan ◽  
Sadia Talib ◽  
Muhammad Noor ◽  
Khalida Noor
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
New Class ◽  
Special Cases ◽  
Preinvex Functions

In this paper, authors introduce a new extension of ?-convexity called ?- preinvexity and generalize the discussed results by Wu et al. in ?On a new class of convex functions and integral inequalities?. Some special cases are deduced from main results. At the end, a briefly conclusion is given.

scholarly journals A new generalization of some quantum integral inequalities for quantum differentiable convex functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yi-Xia Li ◽  
Muhammad Aamir Ali ◽  
Hüseyin Budak ◽  
Mujahid Abbas ◽  
Yu-Ming Chu
Keyword(s):  
Integral Inequality ◽  
Convex Functions ◽  
Integral Identity ◽  
Integral Inequalities ◽  
Quantum Integral ◽  
Special Cases

AbstractIn this paper, we offer a new quantum integral identity, the result is then used to obtain some new estimates of Hermite–Hadamard inequalities for quantum integrals. The results presented in this paper are generalizations of the comparable results in the literature on Hermite–Hadamard inequalities. Several inequalities, such as the midpoint-like integral inequality, the Simpson-like integral inequality, the averaged midpoint–trapezoid-like integral inequality, and the trapezoid-like integral inequality, are obtained as special cases of our main results.

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 Fractional trapezium type inequalities for twice differentiable preinvex functions and their applications

2020 ◽  
Vol 10 (2) ◽  
pp. 226-236
Author(s):  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Integral Operator ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Recent Past ◽  
Trapezium Type ◽  
Special Means ◽  
Special Cases ◽  
Type Integral ◽  
Preinvex Functions ◽  
Almost All

Trapezoidal inequalities for functions of divers natures are useful in numerical computations. The authors have proved an identity for a generalized integral operator via twice differentiable preinvex function. By applying the established identity, the generalized trapezoidal type integral inequalities have been discovered. It is pointed out that the results of this research provide integral inequalities for almost all fractional integrals discovered in recent past decades. Various special cases have been identified. Some applications of presented results to special means have been analyzed. The ideas and techniques of this paper may stimulate further research.

scholarly journals Some New Postquantum Integral Inequalities

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Yu-Ming Chu ◽  
Muhammad Uzair Awan ◽  
Sadia Talib ◽  
Sabah Iftikhar ◽  
Latifa Riahi
Keyword(s):  
Integral Identity ◽  
Integral Inequalities ◽  
Auxiliary Result ◽  
Special Cases ◽  
Preinvex Functions

The goal of this paper is to derive a new generalized postquantum integral identity. Using this new identity as an auxiliary result, we derive some new variants of integral inequalities using p , q -differentiable preinvex functions. We also point out some special cases of the obtained results which show that our results are quite unifying ones.

scholarly journals Some New q—Integral Inequalities Using Generalized Quantum Montgomery Identity via Preinvex Functions

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 553 ◽  
Author(s):  
Miguel Vivas-Cortez ◽  
Artion Kashuri ◽  
Rozana Liko ◽  
Jorge E. Hernández Hernández
Keyword(s):  
Integral Inequalities ◽  
Montgomery Identity ◽  
Quantum Calculus ◽  
Special Cases ◽  
Preinvex Functions

In this work the authors establish a new generalized version of Montgomery’s identity in the setting of quantum calculus. From this result, some new estimates of Ostrowski type inequalities are given using preinvex functions. Given the generality of preinvex functions, particular q —integral inequalities are established with appropriate choice of the parametric bifunction. Some new special cases from the main results are obtained and some known results are recaptured as well. At the end, a briefly conclusion is given.

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 integral inequalities for approximately h—convex functions and their applications

2021 ◽  
Vol 40 (2) ◽  
pp. 481-504
Author(s):  
Artion Kashuri ◽  
Muhammad Raees ◽  
Matloob Anwar
Keyword(s):  
Convex Function ◽  
Integral Inequality ◽  
Convex Functions ◽  
Integral Inequalities ◽  
Integral Type ◽  
Special Cases ◽  
Hölder’S Integral Inequality ◽  
Error Estimations

In this paper, by applying the new and improved form of Hölder’s integral inequality called Hölder—Íşcan integral inequality three inequalities of Hermite—Hadamard and Hadamard integral type for (h, d)—convex functions have been established. Various special cases including classes for instance, h—convex, s—convex function of Breckner and Godunova—Levin—Dragomir and strong versions of the aforementioned types of convex functions have been identified. Some applications to error estimations of presented results have been analyzed. At the end, a briefly conclusion is given.

scholarly journals On Hermite-Hadamard type integral inequalities for n-times differentiable log-preinvex functions

Filomat ◽  
2015 ◽  
Vol 29 (7) ◽  
pp. 1651-1661 ◽  
Author(s):  
M.A. Latif ◽  
S.S. Dragomir
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Type Integral ◽  
Preinvex Functions

In this paper, new Hermite-Hadamard type inequalities for n-times differentiable log-preinvex functions are established. The established results generalize some of those results proved in recent papers for differentiable log-preinvex functions and differentiable log-convex functions.

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