Hogat Allah Amiri Kayvanloo, Mahnaz Khanehgir, Reza Allahyari,
Volume 7, Issue 2 (Vol.7, No. 2, 2021)
Abstract
In this paper, we introduce a Fréchet space and define a measure of noncompactness on it. For credit and the application to our theorems, in the application section of this paper, we present a theorem which shows the existence of solution of infinite system of nonlinear Volterra integral equations, and by using the technique of measures of noncompactness together Darbo fixed point theorem we guarantee the existence of solution in this Fréchet space . Finally, we present some examples which show the efficiency and applicability of our theorem.
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Mahnaz Khanehgir, Reza Allahyari,
Volume 7, Issue 4 (Vol. 7,No. 4, 2021)
Abstract
In this paper, first by using the constructions of probabilistic b-metric Menger space and probabilistic metric like Menger space, we introduce probabilistic b-metric like Menger space and present some examples of it. Then, we state and prove some fixed point theorems for teta-eta contraction multivalued mappings in these spaces. We show some fixed point results for generalized gamma-beta contraction type mappings on the probabilistic b-metric like Menger space. Finally, we present an example of usefulness and applicability of our results.
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