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<p>In this paper, we establish new fixed point results for a class of hybrid operator equations involving the sum and product of three operators defined on RWC-Banach algebras. The basic tools exploited in our investigations are the RWC-property and the concept of the De Blasi measure of weak noncompactness. Our results extend and generalize several well-known theorems proved in Banaś and Taoudi (Taiwan J Math 18:871–893, 2014), Ben Amara et al. (J Math Anal Appl 520:126865, 2022), Krichen and Mefteh (Fixed Point Theory, 2018), Mefteh (Ricerche mat 22:603–611, 2021) and improve some results in Banaś et al. (Filomat 34:2763–2784, 2020), Banaś and Taoudi (2014), Ben Amar et al. (J Funct Anal 259:2215–2237, 2010), Ben Amara et al. (2022), Jeribi et al. (Turk J Math 40:283–291, 2016), Krichen and Mefteh (2018)] by eliminating some assumptions previously required in the literature. These findings are applied to prove the existence of solutions of a large class for nonlinear functional integral equations in the Banach algebra <i>C</i>(<i>J</i>,&#xa0;<i>X</i>), where <i>X</i> is a RWC-Banach algebra. An illustrative example of infinite systems of integral equations on an <i>RWC</i>-Banach algebra, which is not a WC-Banach algebra, is proved.</p>

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Generalized Extension of Hybrid Fixed Point Results in WC-Banach Algebras to RWC-Banach Algebras

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月20日

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  • Khaled Ben Amara,
  • Aref Jeribi,
  • Najib Kaddachi

摘要

In this paper, we establish new fixed point results for a class of hybrid operator equations involving the sum and product of three operators defined on RWC-Banach algebras. The basic tools exploited in our investigations are the RWC-property and the concept of the De Blasi measure of weak noncompactness. Our results extend and generalize several well-known theorems proved in Banaś and Taoudi (Taiwan J Math 18:871–893, 2014), Ben Amara et al. (J Math Anal Appl 520:126865, 2022), Krichen and Mefteh (Fixed Point Theory, 2018), Mefteh (Ricerche mat 22:603–611, 2021) and improve some results in Banaś et al. (Filomat 34:2763–2784, 2020), Banaś and Taoudi (2014), Ben Amar et al. (J Funct Anal 259:2215–2237, 2010), Ben Amara et al. (2022), Jeribi et al. (Turk J Math 40:283–291, 2016), Krichen and Mefteh (2018)] by eliminating some assumptions previously required in the literature. These findings are applied to prove the existence of solutions of a large class for nonlinear functional integral equations in the Banach algebra C(J, X), where X is a RWC-Banach algebra. An illustrative example of infinite systems of integral equations on an RWC-Banach algebra, which is not a WC-Banach algebra, is proved.