Fixed Point Theory for Multivalued Integral Contractions in \(\vartheta_{\nu}^{\ell}\)-Metric Spaces with Geometric and Applied Perspectives

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DOI: https://doi.org/10.28924/2291-8639-24-2026-172
Published: May 29, 2026
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Mohammad H.M. Rashid, Rabaa Almaita, Fixed Point Theory for Multivalued Integral Contractions in \(\vartheta_{\nu}^{\ell}\)-Metric Spaces with Geometric and Applied Perspectives, Int. J. Anal. Appl., 24 (2026), 172.

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Mohammad H.M. Rashid, Rabaa Almaita

Abstract

Here, we propose a complete fixed point theory for set-valued mappings possessing integral-type contractive conditions in \(\vartheta_{\nu}^{\ell}\)-metric spaces-a novel extension of the traditional notion of metric spaces proposed very recently by Joshi and co-authors. With the aid of some auxiliary concepts like \(\alpha\)-admissible mappings, together with integral-type contraction conditions, we establish some new results on the existence and uniqueness of fixed points of set-valued mappings that not only generalize but also merge several fundamental theorems in the literature, particularly those by Branciari, Nadler, and Mizoguchi-Takahashi. In addition to the existence issues, we consider the structure of the set of fixed points through the concepts of fixed circle and fixed disc, providing thus more detailed information about the position of the fixed points. To substantiate our theoretical findings, we provide various applications in solving three different classes of problems, namely, differential inclusions, fractional partial differential equations, and Volterra integro-differential equations.

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