Some Nonlinear Integral Inequalities Connected with Retarded Terms on Time Scales

The objective of this research is to formulate a specific class of integral inequalities of Gronwall kind concerning retarded term and nonlinear integrals with time scales theory. Our results generate several new inequalities that reflect continuous and discrete form, as well as giving the unknown function an upper bound estimate. The effectiveness of such inequalities arises from the belief that it is widely relevant in unique circumstances where there is no valid utilization of various available inequalities. Applications are additionally represented to display the legitimacy of built-up hypotheses.

Hölder type integral inequalities with different pseudo-operations

The theory of non-additive measures and relevant nonlinear integrals has recently been developed as a new branch of mathematics with various applications in other sciences. In this area, pseudo-additive measures and pseudo-integrals play important roles as new extensions of measures and integrals. The aim of this paper is to prove Hölder type integral inequalities with different pseudo-operations. Several examples are given to show the inequalities in more tangible forms.