Generalized Contractions in \(C^*\)-Algebra-Valued Extended \(b\)-Suprametric Spaces with Applications

Information from the abstract

In this contribution, we develop a relaxed fixed-point (FP) for nonlinear operators in \(C^*\)-algebra-valued extended \(b\)-suprametric spaces (C*-AVEbSMS). We propose a novel class of control functions \(\Theta_R\) that allows strictly increasing but not necessarily continuous behavior, thereby extending the classical \(\vartheta\)-contraction framework. Moreover, various relaxed \(\vartheta_R\)-type contractive conditions are established using max-type \(C^*\)-algebra-valued functionals. Under suitable conditions, including a jump condition on the control function, the uniqueness and existence of (FP) are obtained in complete spaces (CM). Examples are presented to validate the applicability of the outcomes and to emphasize the role of discontinuities in the convergence process. As applications, we study nonlinear differential models, including a second-order particle motion problem and a fourth-order beam equation, and show that the corresponding integral operators admit signal solution within the formulate framework.

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Related topics: Fixed Point Theorems Analysis · Functional Equations Stability Results · Approximation Theory and Sequence Spaces