In this study, we introduce a new conformable derivative, namely the beta-conformable derivative. We derive Taylor?s theorem for also investigate some properties of and useful related theorems light operator, extend recent classical integral inequalities including Steffensen Hermite-Hadamard inequality.

We introduce the normalized Jensen-Mercer functional Mn( f ,x, p) = f (a)+ f (b)− n ∑ i=1 pi f (xi)− f ( a+b− n ∑ i=1 pixi ) and establish the inequalities of type MMn( f ,x,q) Mn( f ,x, p) mMn( f ,x,q) , where f is a convex function, x = (x1, . . . ,xn) and m and M are real numbers satisfying certain conditions. We prove them for the case when p and q are nonnegative n -tuples and when p and q...

* Correspondence: [email protected] Abdus Salam School of Mathematical Sciences, GC University, 68-b, New Muslim Town, Lahore 54600, Pakistan Full list of author information is available at the end of the article Abstract In this paper, we extend some old and give some new refinements of the JensenSteffensen inequality. Further, we investigate the log-convexity and the exponential conve...

There are a number of results that provide bounds for integrals of products of functions. The main techniques that shall be employed in the current article involve the Steffensen inequality and a variety of bounds related to the Čebyšev functional. There have been some developments in both of these in the recent past with which the current author has been involved. These have been put to fruitf...

Building on the work of Josip Pečarić in 2013 and 1982 Srivastava 2017. We prove some new α-conformable dynamic inequalities Steffensen-type time scales. In case when α=1, we obtain well-known scale due to Steffensen inequalities. For specific scales, further show relevant as special cases: integral discrete Symmetry plays an essential role determining correct methods solve