Muhammad Adil Khan

Some new inequalities of Hermite-Hadamard type for s-convex functions with applications

Abstract In this paper, we present several new and generalized Hermite-Hadamard type inequalities for s-convex as well as s-concave functions via classical and Riemann-Liouville fractional integrals. As applications, we provide new error estimations for the trapezoidal formula.

Around Jensen’s inequality for strongly convex functions

In this paper we use basic properties of strongly convex functions to obtain new inequalities including Jensen type and Jensen–Mercer type inequalities. Applications for special means are pointed out as well. We also give a Jensen’s operator inequality for strongly convex functions. As a corollary, we improve the Hölder-McCarthy inequality under suitable conditions. More precisely we show that if

Improvement of Jensen's Inequality in terms of Gâteaux Derivatives for Convex Functions in Linear Spaces with Applications

Sp\left( A \right) \subset \left( 1,\infty \right)

On Zipf–Mandelbrot entropy

SpA⊂1,∞, then

Generalization of Hermite-Hadamard Type Inequalities via Conformable Fractional Integrals

\begin{aligned} {{\left\langle Ax,x \right\rangle }^{r}}\le \left\langle {{A}^{r}}x,x \right\rangle -\frac{{{r}^{2}}-r}{2}\left( \left\langle {{A}^{2}}x,x \right\rangle -{{\left\langle Ax,x \right\rangle }^{2}} \right) ,\quad r\ge 2 \end{aligned}

Generalized conformable fractional operators

Ax,xr≤Arx,x-r2-r2A2x,x-Ax,x2,r≥2and if