Well-Posedness and Numerical Study for Solutions of a Parabolic Equation with Variable-Exponent Nonlinearities by Jamal H. Al-Smail, Salim A. Messaoudi, Ala A. Talahmeh

“…By using a nonlinear operator theory, we prove the existence and uniqueness of weak solutions under suitable assumptions. …”
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Douglas' Factorization Theorem and Atomic System in Hilbert Pro-$C^{\ast}$-Modules by Mohamed Rossafi, Roumaissae Eljazzar, Ram Mohapatra

“…In the present paper, we introduce  the generalized inverse operators, which have an exciting role in operator theory. We establish Douglas' factorization theorem type  for  the Hilbert pro-$C^{\ast}$-module.We introduce the notion of atomic system and $K$-frame in the Hilbert pro-$C^{\ast}$-module and study their relationship. …”
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On absolutely invertibles by Francisco Javier García-Pacheco, María de los Ángeles Moreno-Frías, Marina Murillo-Arcila

“…Finally, two applications to classical operator theory were provided, i.e., every Banach space of dimension of at least $ 2 $ could be equivalently re-normed in such a way that the group of surjective linear isometries was not a normal subgroup of the group of isomorphisms, and every infinite-dimensional Banach space, containing a proper complemented subspace isomorphic to it, could be equivalently re-normed so that the set of surjective linear operators was not dense in the Banach algebra of bounded linear operators.…”
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Solving a system of Caputo-Hadamard fractional differential equations via Perov’s fixed point theorem by Nouar Aziza Souad, Nisse Khadidja, Beloul Said

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Bipartite polygon models: entanglement classes and their nonlocal behaviour by Mayalakshmi Kolangatt, Thigazholi Muruganandan, Sahil Gopalkrishna Naik, Tamal Guha, Manik Banik, Sutapa Saha

“…In this paper, we investigate Hardy's nonlocal behavior within a broad class of operational theories, including the qubit state space as a specific case. …”
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