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Krasnosel’skii-type fixed point theorems for convex-power condensing mappings in locally convex spaces

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Abstract

In this paper, we prove some fixed point theorems for the sum \(T+S\) of two nonlinear mappings acting on a locally convex space, where S is a contraction (nonexpansive or expansive) and T is S-convex-power condensing. Our fixed point results extend several earlier works. As an application, we investigate the solvability of a class of nonlinear Volterra integral equations in locally convex spaces.

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Acknowledgements

The authors would like to thank the Editor and the Referee for their careful reading of the manuscript. Their constructive comments and suggestions markedly improved the quality of the paper.

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Authors and Affiliations

  1. Département de Mathématiques, Faculté des Sciences Semlalia, Université Cadi Ayyad, B. P. 2390, Marrakech, Morocco

    Abdelmjid Khchine & Lahcen Maniar

  2. National School of Applied Sciences, Cadi Ayyad University, Marrakech, Morocco

    Mohamed Aziz Taoudi

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  1. Abdelmjid Khchine
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  2. Lahcen Maniar
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  3. Mohamed Aziz Taoudi
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Correspondence to Abdelmjid Khchine.

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Khchine, A., Maniar, L. & Taoudi, M.A. Krasnosel’skii-type fixed point theorems for convex-power condensing mappings in locally convex spaces. J. Fixed Point Theory Appl. 19, 2985–3012 (2017). https://doi.org/10.1007/s11784-017-0465-6

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