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Fixed point theorems for the sum of (ws)-compact and asymptotically \({\Phi}\)-nonexpansive mappings

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Abstract

In this paper, we introduce the concept of an asymptotically \({\Phi}\)-nonexpansive operator. In addition, we establish some Krasnoselskiitype fixed point theorems for the sum of two operators A and B, where the operator A is assumed to be (ws)-compact, and B is a (ws)-compact and asymptotically \({\Phi}\)-nonexpansive operator on an unbounded closed convex subset of a Banach space. Also we present Leray–Schauder alternatives and Furi–Pera-type fixed point theorems for the sum of two (ws)-compact mappings.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, Sfax University, Sfax, LA, 1171, 3000, Tunisia

    Afif Ben Amar & Amel Touati

  2. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland

    Donal O’Regan

Authors
  1. Afif Ben Amar
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  2. Donal O’Regan
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  3. Amel Touati
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Correspondence to Afif Ben Amar.

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Ben Amar, A., O’Regan, D. & Touati, A. Fixed point theorems for the sum of (ws)-compact and asymptotically \({\Phi}\)-nonexpansive mappings. J. Fixed Point Theory Appl. 18, 771–784 (2016). https://doi.org/10.1007/s11784-016-0326-8

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  • DOI: https://doi.org/10.1007/s11784-016-0326-8

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