Fixed point theorems for the sum of two operators on unbounded convex sets and an application


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	Fixed point theorems for the sum of two operators on unbounded convex sets and an application


	Fixed Point Theory, Volume 19, No. 2, 2018, 435-448, June 1st, 2018 DOI: 10.24193/fpt-ro.2018.2.34 Authors: Afif Ben Amar and Amel Touati Abstract: In this paper, we establish new fixed point results for the sum of two operators A and B, where the operator A is assumed to be weakly compact and (ws)-compact, while B is a weakly condensing and expansive operator defined on unbounded domains under different boundary conditions as well as other additional assumptions. In addition, we get new generalized forms of the Krasnosel'skii fixed point theorem in a Banach space by using the concept of measure of weak noncompactness of De Blasi. Later on, we give an application to solve a nonlinear Hammerstein integral equation in L¹-space. Key Words and Phrases: (ws)-compact, weakly condensing, expansive operator, measure of weak noncompactness, fixed point theorems. 2010 Mathematics Subject Classification: 47H10, 47J05, 47J10. Published on-line: June 1st, 2018. Abstract pdf Fulltext pdf Back to volume's table of contents