Relative h-preinvex functions and integral inequalities

2020 ◽  
Vol 27 (2) ◽  
pp. 285-295
Author(s):  
Marian Matłoka
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
New Class ◽  
Preinvex Functions ◽  
New Inequalities

AbstractIn this paper, we consider a new class of convex functions, called relative h-preivex functions. Seven new inequalities of Hermite–Hadamard type for relative h-preinvex functions are established using different approaches.

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 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 Simpson type integral inequalities for convex functions via Riemann-Liouville integrals

Filomat ◽  
2017 ◽  
Vol 31 (14) ◽  
pp. 4415-4420 ◽  
Author(s):  
Erhan Set ◽  
Ahmet Akdemir ◽  
Emin Özdemir
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Type Integral ◽  
Derivatives Of ◽  
New Inequalities

In this paper some new inequalities of Simpson-type are established for the classes of functions whose derivatives of absolute values are convex functions via Riemann-Liouville integrals. Also, by special selections of n, we give some reduced results.

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 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.

scholarly journals Some new inequalities via s-convex functions on time scales

2021 ◽  
Vol 13 (1) ◽  
pp. 239-257
Author(s):  
Naila Mehreen ◽  
Matloob Anwar
Keyword(s):  
Convex Function ◽  
Time Scales ◽  
Convex Functions ◽  
Time Scale ◽  
Integral Inequalities ◽  
New Inequalities

Abstract In this paper, we prove some new integral inequalities for s-convex function on time scale. We give results for the case when time scale is ℝ and when time scale is ℕ.

scholarly journals Tempered Fractional Integral Inequalities for Convex Functions

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 500 ◽  
Author(s):  
Gauhar Rahman ◽  
Kottakkaran Sooppy Nisar ◽  
Thabet Abdeljawad
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Special Cases ◽  
New Inequalities

Certain new inequalities for convex functions by utilizing the tempered fractional integral are established in this paper. We also established some new results by employing the connections between the tempered fractional integral with the (R-L) fractional integral. Several special cases of the main result are also presented. The obtained results are more in a general form as it reduced certain existing results of Dahmani (2012) and Liu et al. (2009) by employing some particular values of the parameters.

scholarly journals On New Inequalities via Riemann-Liouville Fractional Integration

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Mehmet Zeki Sarikaya ◽  
Hasan Ogunmez
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Fractional Integration ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
New Inequalities

We extend the Montgomery identities for the Riemann-Liouville fractional integrals. We also use these Montgomery identities to establish some new integral inequalities. Finally, we develop some integral inequalities for the fractional integral using differentiable convex functions.

scholarly journals New Conformable Fractional Integral Inequalities of Hermite–Hadamard Type for Convex Functions

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 263 ◽  
Author(s):  
Pshtiwan Mohammed ◽  
Faraidun Hamasalh
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Conformable Fractional Integral ◽  
New Inequalities

In this work, we established new inequalities of Hermite–Hadamard type for convex functions via conformable fractional integrals. Through the conformable fractional integral inequalities, we found some new inequalities of Hermite–Hadamard type for convex functions in the form of classical integrals.

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.

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