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Fixed point theorems for Meir-Keeler condensing nonself-mappings with an application. (English) Zbl 1491.47044

Summary: Fixed point theorems of nonself-mapping Meir-Keeler condensing operator are established in this paper, respectively, under the conditions of Leray-Schauder, Rothe and Altman types which are different from the results for self-mapping in some references. Also, a priori estimate theorem is obtained with application to the existence of solutions for an integral equation of Volterra type.

MSC:

47H10 Fixed-point theorems
47H08 Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc.
45D05 Volterra integral equations
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