HERONIAN MEAN DERIVATIVE-BASED SIMPSON’S-TYPE SCHEME FOR RIEMANN-STIELTJES INTEGRAL

Riemann-Stieltjes type integral based on generated pseudo-operations

We shall consider generated pseudo-operations of the following form: x⊕ y = g(−1) (g(x) + g(y)) , x ̄ y = g(−1) (g(x)g(y)) , where g is a positive strictly monotone generating function and g(−1) is its pseudo-inverse. Using this type of pseudo-operations, the Riemann-Stieltjes type integral will be introduced and investigated.

Some Grüss Type Inequalities for Riemann-stieltjes Integral and Applications

The Riemann-stieltjes Integral on Time Scales

We study the process of integration on time scales in the sense of Riemann-Stieltjes. Analogues of the classical properties are proved for a generic time scale, and examples are given.

A Companion of Ostrowski’s Inequality for the Riemann-stieltjes Integral

Relative Convexity and Quadrature Rules for the Riemann–stieltjes Integral

We develop Trapezoid, Midpoint, and Simpson’s rules for the Riemann-Stieltjes integral, the latter two being new. These rules are completely natural when the notion of relative convexity is used. Mathematics subject classification (2010): 65D30.