scholarly journals New Weighted Hermite–Hadamard Type Inequalities for Differentiable h -Convex and Quasi h -Convex Mappings

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Muhammad Amer Latif
Keyword(s):  
Convex Functions ◽  
Convex Mappings

In this paper, new weighted Hermite–Hadamard type inequalities for differentiable h -convex and quasi h -convex functions are proved. These results generalize many results proved in earlier works for these classes of functions. Applications of some of our results to s ˘ -divergence and to statistics are given.

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.

Refinements of the Hermite–Hadamard inequality for co-ordinated convex mappings

2019 ◽  
Vol 25 (1) ◽  
pp. 73-81 ◽  
Author(s):  
Huseyin Budak ◽  
Fuat Usta ◽  
Mehmet Zeki Sarikaya
Keyword(s):  
Convex Functions ◽  
Recent Progress ◽  
Closed Interval ◽  
Hadamard Inequality ◽  
Convex Mappings

Abstract This paper is motivated by the recent progress on the Hermite–Hadamard inequality for convex functions defined on the bounded closed interval, obtained by Z. Pavić [Z. Pavić, Improvements of the Hermite–Hadamard inequality, J. Inequal. Appl. 2015 2015, Article ID 222]. As a generalization, we obtained a new refinement of the Hermite–Hadamard inequality for co-ordinated convex functions defined on the rectangle.

Hermite–Hadamard–Mercer-Type Inequalities for Harmonically Convex Mappings

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2556
Author(s):  
Xuexiao You ◽  
Muhammad Aamir Ali ◽  
Hüseyin Budak ◽  
Jiraporn Reunsumrit ◽  
Thanin Sitthiwirattham
Keyword(s):  
Convex Functions ◽  
Absolute Value ◽  
Convex Mappings ◽  
Special Means ◽  
Harmonically Convex Functions

In this paper, we prove Hermite–Hadamard–Mercer inequalities, which is a new version of the Hermite–Hadamard inequalities for harmonically convex functions. We also prove Hermite–Hadamard–Mercer-type inequalities for functions whose first derivatives in absolute value are harmonically convex. Finally, we discuss how special means can be used to address newly discovered inequalities.

Certain results on starlike and convex functions

2020 ◽  
Vol 4 (2) ◽  
pp. 1-14
Author(s):  
Pardeep Kaur ◽  
◽  
Sukhwinder Singh Billing ◽  
Keyword(s):  
Convex Functions ◽  
Starlike And Convex Functions

Some new generalizations for GA-convex functions

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 1009-1016 ◽  
Author(s):  
Ahmet Akdemir ◽  
Özdemir Emin ◽  
Ardıç Avcı ◽  
Abdullatif Yalçın
Keyword(s):  
Convex Functions ◽  
Integral Identity ◽  
Integral Inequalities ◽  
General Integral ◽  
Second Derivatives ◽  
Derivatives Of

In this paper, firstly we prove an integral identity that one can derive several new equalities for special selections of n from this identity: Secondly, we established more general integral inequalities for functions whose second derivatives of absolute values are GA-convex functions based on this equality.

Hermite-Hadamard and simpson-like type inequalities for differentiable p-quasi-convex functions

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 5945-5953 ◽  
Author(s):  
İmdat İsçan ◽  
Sercan Turhan ◽  
Selahattin Maden
Keyword(s):  
Convex Functions ◽  
Real Numbers ◽  
Absolute Value ◽  
Special Means ◽  
Quasi Convexity

In this paper, we give a new concept which is a generalization of the concepts quasi-convexity and harmonically quasi-convexity and establish a new identity. A consequence of the identity is that we obtain some new general inequalities containing all of the Hermite-Hadamard and Simpson-like type for functions whose derivatives in absolute value at certain power are p-quasi-convex. Some applications to special means of real numbers are also given.

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