This work introduces tvs-valued cone suprametric spaces and establishes fixed-point theorems, suggesting significant applications in fractional differential equations.
The main aim of this work is to introduce the notion of a tvs-valued cone suprametric space,which unifies and generalizes cone suprametric spaces, tvs-valued cone metric spaces, and cone metric spaces, and to establish new fixed point theorems for single-valued and multivalued generalized contractive mappings within this framework. The presented results extend and unify some well-known outcomes available in the existing literature. To demonstrate the applicability and significance of the proposed theory, a number of illustrative examples are provided. In addition, the obtained fixed point results are employed to investigate the existence of solutions for a Caputo fractional differential equation as well as a Volterra–Fredholm integral equation.
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Alzumi et al. (2026) studied this question.
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