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Fixed Point Theorem via Measure of Non-Compactness for a New Kind of Contractions

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Abstract

In this paper, we will use the notion of \(\alpha \)-admissible mappings in Banach spaces, to introduce the concept of \({{T}_{\beta }}\)-contractive mappings and establish a fixed point theorem for this type of contractions. Our theorems generalize and improve many results in the literature. Moreover, we apply the main result to prove the existence of a solution for Volterra-integral equation, under more general assumptions than previously made.

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Authors and Affiliations

  1. Sultan Moulay Slimane University, 23000, Beni-Mellal, Morocco

    Youssef Touail, Amine Jaid & Driss El Moutawakil

Authors
  1. Youssef Touail
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  2. Amine Jaid
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  3. Driss El Moutawakil
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Correspondence to Youssef Touail.

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Touail, Y., Jaid, A. & El Moutawakil, D. Fixed Point Theorem via Measure of Non-Compactness for a New Kind of Contractions. Vestnik St.Petersb. Univ.Math. 56, 198–202 (2023). https://doi.org/10.1134/S1063454123020164

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  • DOI: https://doi.org/10.1134/S1063454123020164

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