This paper is concerned with the equational logic of corecursion, that is of definitions involving final coalgebra maps. The framework for our study is iteration theories (cf. e.g. Bloom and Ésik [?, ?]), recently re-introduced as models of the FLR0 fragment of the Formal Language of Recursion [?, ?, ?]. We present a new class of iteration theories derived from final coalgebras. This allows us ...

(A map is locally compact if every point has a neighborhood whose image is precompact.) Theorem 1 for maps is thus a special case of this result. In fact, the results in [2] go far beyond Theorem 2 and are concerned with finding very general circumstances in which the Lefschetz fixed point theorem applies. Further important work in this area appears in [1], [3], [4]. Srzednicki proved the follo...

In this article, we employ the Tarski’s fixed point theorem to establish the existence of extremal solutions for fractional differential equations with maxima.

This paper is concerned with the existence of travelling wave solutions in a class of delayed reaction–diffusion systems without monotonicity, which concludes two-species diffusion–competition models with delays. Previous methods do not apply in solving these problems because the reaction terms do not satisfy either the so-called quasimonotonicity condition or non-quasimonotonicity condition. B...

Temporal logics over finite traces are not the same as temporal logics over potentially infinite traces. We propose that existing methods for proving deductive completeness for infinite-trace logics are effective on their finite counterparts. To adapt proofs for infinite-trace logics, we “inject” finiteness: that is, we alter the proof structure to ensure that models are finite. As evidence for...

Darbo's fixed point theorem and its generalizations play a crucial role in the existence of solutions in integral equations. Meir-Keeler condensing operators is a generalization of Darbo's fixed point theorem and most of other generalizations are a special case of this result. In recent years, some authors applied these generalizations to solve several special integral equations and some of the...

In this paper, we improve some recent coupled fixed point resultsfor single-valued operators in the framework of ordered $b$-metricspaces established by Bota et al. [M-F. Bota, A. Petrusel, G.Petrusel and B. Samet, Coupled fixed point theorems forsingle-valued operators in b-metric spaces, Fixed Point TheoryAppl. (2015) 2015:231]. Also, we prove that Perov-type fix...

In this paper, we discuss and extend some recent common fixed point results established by using $varphi-$weakly contractive mappings. A very important step in the development of the fixed point theory was given by A.H. Ansari by the introduction of a $C-$class function. Using $C-$class functions, we generalize some known fixed point results. This type of functions is a very important class of ...