Affiliation:
1. Higher School of Sciences and Technology, Departement of Mathematics, University of Sousse, Tunisia
Abstract
Motivated by the open question posed by H. K. XU in [39] (Question 2:8),
Belhadj, Ben Amar and Boumaiza introduced in [5] the concept of Meir-Keeler
condensing operator for self-mappings in a Banach space via an arbitrary
measure of weak noncompactness. In this paper, we introduce the concept of
Meir- Keeler condensing operator for nonself-mappings in a Banach space via
a measure of weak noncompactness and we establish fixed point results under
the condition of Leray-Schauder type. Some basic hybrid fixed point theorems
involving the sum as well as the product of two operators are also
presented. These results generalize the results on the lines of
Krasnoselskii and Dhage. An application is given to nonlinear hybrid
linearly perturbed integral equations and an example is also presented.
Publisher
National Library of Serbia
Cited by
2 articles.
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