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In this paper, we study the relationship between the class of weakly demicompact linear operators, introduced in [KRICHEN, B.—O'REGAN, D.: On the class of relatively weakly demicompact nonlinear operators, Fixed Point Theory 19 (2018), 625–630], and measures of weak noncompactness of linear operators with respect to an axiomatic one. Moreover, some Fredholm and perturbation results involving the class of weakly demicompact linear operators are investigated. Our results are then used to investigate the relationship between the relative essential spectrum of the sum of two linear operators and the relative essential spectrum of each of these operators. [ABSTRACT FROM AUTHOR]

In this paper, we consider the concept of the so-called generalized metric space and give some results on the existence, uniqueness and estimation of the solutions of Fredholm type integro- differential equations in two variables using Perov's fixed point theorem. Furthermore, we give some illustrative examples to verify the effectiveness and applicability of our main result. [ABSTRACT FROM AUTHOR]

In this paper by using of Suzuki-type approach we introduce the new contractive condition in the framework of non-Archimedean fuzzy metric spaces. We prove also the corresponding coincidence fixed point theorem for two mappings in this framework. Finally, two examples are presented to verify the effectiveness and applicability of our main results. [ABSTRACT FROM AUTHOR]