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 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 Hardy-Type Inequalities on Time Scale via Convexity in Several Variables

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Tzanko Donchev ◽  
Ammara Nosheen ◽  
Josip Pečarić
Keyword(s):  
Time Scales ◽  
Convex Functions ◽  
Time Scale ◽  
Hardy Type Inequalities ◽  
Arbitrary Time ◽  
Hardy Type ◽  
Several Variables ◽  
New Inequalities

We extend some Hardy-type inequalities with general kernels to arbitrary time scales using multivariable convex functions. Some classical and new inequalities are deduced seeking applications.

scholarly journals Hermite-Hadamard Type Inequalities Associated with Coordinated((s,m),QC)-Convex Functions

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Yu-Mei Bai ◽  
Shan-He Wu ◽  
Ying Wu
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Integral Inequalities ◽  
Type Integral ◽  
Definition Of

In this paper, we introduce the definition of coordinated((s,m),QC)-convex function and establish some Hermite-Hadamard type integral inequalities for coordinated((s,m),QC)-convex functions.

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 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 Some Dynamic Inequalities via Diamond Integrals for Function of Several Variables

2021 ◽  
Vol 5 (4) ◽  
pp. 207
Author(s):  
Muhammad Bilal ◽  
Khuram Ali Khan ◽  
Hijaz Ahmad ◽  
Ammara Nosheen ◽  
Khalid Mahmood Awan ◽  
...  
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Jensen’S Inequality ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Several Variables ◽  
Time Scale Calculus ◽  
Special Cases ◽  
Function Of Several Variables ◽  
New Inequalities

In this paper, Jensen’s inequality and Fubini’s Theorem are extended for the function of several variables via diamond integrals of time scale calculus. These extensions are used to generalize Hardy-type inequalities with general kernels via diamond integrals for the function of several variables. Some Hardy Hilbert and Polya Knop type inequalities are also discussed as special cases. Classical and new inequalities are deduced from the main results using special kernels and particular time scales.

scholarly journals On Hadamard Type Fractional Inequalities for Riemann–Liouville Integrals via a Generalized Convexity

2022 ◽  
Vol 6 (1) ◽  
pp. 28
Author(s):  
Tao Yan ◽  
Ghulam Farid ◽  
Hafsa Yasmeen ◽  
Chahn Yong Jung
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Generalized Convexity ◽  
Monotone Function ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Recent Past ◽  
Hadamard Inequality

In the literature of mathematical inequalities, convex functions of different kinds are used for the extension of classical Hadamard inequality. Fractional integral versions of the Hadamard inequality are also studied extensively by applying Riemann–Liouville fractional integrals. In this article, we define (α,h−m)-convex function with respect to a strictly monotone function that unifies several types of convexities defined in recent past. We establish fractional integral inequalities for this generalized convexity via Riemann–Liouville fractional integrals. The outcomes of this work contain compact formulas for fractional integral inequalities which generate results for different kinds of convex functions.

scholarly journals Some Estimates for Generalized Riemann-Liouville Fractional Integrals of Exponentially Convex Functions and Their Applications

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 807 ◽  
Author(s):  
Saima Rashid ◽  
Thabet Abdeljawad ◽  
Fahd Jarad ◽  
Muhammad Aslam Noor
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Fractional Integrals ◽  
Order Derivative ◽  
Fundamental Identity ◽  
First Order ◽  
Special Means ◽  
Exponentially Convex Functions ◽  
New Inequalities

In the present paper, we investigate some Hermite-Hadamard ( HH ) inequalities related to generalized Riemann-Liouville fractional integral ( GRLFI ) via exponentially convex functions. We also show the fundamental identity for GRLFI having the first order derivative of a given exponentially convex function. Monotonicity and exponentially convexity of functions are used with some traditional and forthright inequalities. In the application part, we give examples and new inequalities for the special means.

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.

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