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We obtain a principal topology and some related results. We also give some hints of possible applications. Some mathematical systems are both lattice and topological space. We show that a topology defined on the any bounded lattice is definable in terms of uninorms. Also, we see that these topologies satisfy the condition of the principal topology. These topologies can not be metrizable except for the discrete metric case. We show an equivalence relation on the class of uninorms on a bounded lattice based on equality of the topologies induced by uninorms. [ABSTRACT FROM AUTHOR]

In this paper, we gave adjustments for some results in the paper [1], and proved three new Katugampola fractional Hermite-Hadamard type inequalities for convex functions by using the left and the right fractional integrals independently. One of our Katugampola fractional Hermite-Hadamard type inequalities is better than given by Chen and Katugampola. Also, we gave two new Katugampola fractional identities for differentiable functions. By using these identities, we obtained some new trapezoidal type inequalities for convex functions. Our results generalize earlier results. [ABSTRACT FROM AUTHOR]

In the study, we introduce the definition of a locally internal uninorm on an arbitrary bounded lattice L. We examine some properties of an idempotent and locally internal uninorm on an arbitrary bounded latice L, and investigate relationship between these operators. Moreover, some illustrative examples are added to show the connection between idempotent and locally internal uninorm. [ABSTRACT FROM AUTHOR]