On Integral Inequalities Involving Generalized Lipschitzian Functions

A new class of mappings that includes the class of Lipschitzian mappings is introduced. For this kind of mappings, new integral inequalities of Hadamard’s type are obtained. Our results are extensions of many previous contributions related to integral inequalities for Lipschitzian mappings.

Local Sharp Vector Variational Type Inequality and Optimization Problems

In this paper, our goal was to establish the relationship between solutions of local sharp vector variational type inequality and sharp efficient solutions of vector optimization problems, also Minty local sharp vector variational type inequality and sharp efficient solutions of vector optimization problems, under generalized approximate η-convexity conditions for locally Lipschitzian functions.

Improved error estimate and applications of the complete quartic spline

In this paper an improved error bound is obtained for the complete quartic spline with deficiency 2, in the less smooth class of continuous functions. In the case of Lipschitzian functions, the obtained estimate improves the constant from Theorem 3, in J. Approx. Theory 58 (1989) 58-67. Some applications of the complete quartic spline in the numerical integration and in the construction of an iterative numerical method for fourth order two-point boundary value problems with pantograph type delay are presented.

Some new integral inequalities for Lipschitzian functions

This paper is about obtaining some new type of integral inequalities for functions from the Lipschitz class. For this, some new integral inequalities related to the differences between the two different types of integral averages for Lipschitzian functions are obtained. Moreover, applications for some special means as arithmetic, geometric, logarithmic, -logarithmic, harmonic, identric are given.

Fejér-type inequalities for Lipschitzian functions and their applications

In this paper, we shall establish some Fej?r-type inequalities for L-Lipschitzian functions. These inequalities can connect with Fej?r inequality (1). Also, some applications to convex function, ?-th moment, mathematical expectation of a random variable and Euler?s Beta function are provided.

Inequalities of Čebyšev Type for Lipschitzian Functions in Banach Algebras

In this paper we give some Čebyšev type norm inequalities for two Lipschitzian functions on Banach algebras. Some examples for power function, exponential and the resolvent functions are also provided