scholarly journals New Inequalities of Simpson’s type for differentiable functions via generalized convex function

2021 ◽  
Vol 359 (2) ◽  
pp. 137-147
Author(s):  
Shan E. Farooq ◽  
Khurram Shabir ◽  
Shahid Qaisar ◽  
Farooq Ahmad ◽  
O. A. Almatroud
Keyword(s):  
Convex Function ◽  
Differentiable Functions ◽  
New Inequalities

scholarly journals Schur-Power Convexity of a Completely Symmetric Function Dual

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 897 ◽  
Author(s):  
Huan-Nan Shi ◽  
Wei-Shih Du
Keyword(s):  
Convex Function ◽  
Symmetric Function ◽  
Symmetric Functions ◽  
New Inequalities

In this paper, by applying the decision theorem of the Schur-power convex function, the Schur-power convexity of a class of complete symmetric functions are studied. As applications, some new inequalities are established.

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 New integral inequalities for differentiable functions

2003 ◽  
Vol 34 (3) ◽  
pp. 249-253
Author(s):  
B. G. Pachpatte
Keyword(s):  
Integral Inequalities ◽  
Differentiable Functions ◽  
Special Cases ◽  
New Inequalities

The object of this paper is to establish new integral inequalities involving two functions and their derivatives. Our results in the special cases yield some well known inequalities in the literature and also other new inequalities.

scholarly journals Some new Ostrowski and Gr"Uss type inequalities

2007 ◽  
Vol 38 (2) ◽  
pp. 111-120 ◽  
Author(s):  
B. G. Pachpatte
Keyword(s):  
Differentiable Functions ◽  
Second Derivatives ◽  
Integral Identities ◽  
New Inequalities

In this paper we establish some new inequalities of Ostrowski and Gr"uss type, involving three functions whose second derivatives are bounded. The analysis used in the proofs is fairly elementary and based on the integral identities for twice differentiable 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.

New inequalities for $n$-time differentiable functions

2019 ◽  
Vol 12 (2) ◽  
pp. 1-15
Author(s):  
Çetin Yildiz ◽  
M. Emin Özdemir
Keyword(s):  
Differentiable Functions ◽  
New Inequalities

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.

Estimation of different entropies via Abel–Gontscharoff Green functions and Fink’s identity using Jensen type functionals

2018 ◽  
Vol 26 (1/2) ◽  
pp. 15-39
Author(s):  
Khuram Ali Khan ◽  
Tasadduq Niaz ◽  
Đilda Pečarić ◽  
Josip Pečarić
Keyword(s):  
Convex Function ◽  
Shannon Entropy ◽  
Green Functions ◽  
Fink’S Identity ◽  
New Inequalities

In this work, we estimated the different entropies like Shannon entropy, Rényi divergences, Csiszár divergence by using Jensen’s type functionals. The Zipf’s–Mandelbrot law and hybrid Zipf’s–Mandelbrot law are used to estimate the Shannon entropy. The Abel–Gontscharoff Green functions and Fink’s Identity are used to construct new inequalities and generalized them for m-convex function.

scholarly journals Quantum Hermite–Hadamard-type inequalities for functions with convex absolute values of second $q^{b}$-derivatives

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Muhammad Aamir Ali ◽  
Hüseyin Budak ◽  
Mujahid Abbas ◽  
Yu-Ming Chu
Keyword(s):  
Convex Functions ◽  
Differentiable Functions ◽  
Right Hand ◽  
Second Derivatives ◽  
New Inequalities

AbstractIn this paper, we obtain Hermite–Hadamard-type inequalities of convex functions by applying the notion of $q^{b}$ q b -integral. We prove some new inequalities related with right-hand sides of $q^{b}$ q b -Hermite–Hadamard inequalities for differentiable functions with convex absolute values of second derivatives. The results presented in this paper are a unification and generalization of the comparable results in the literature on Hermite–Hadamard inequalities.

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