The objective of this research article is to introduce Kikkawa and Suzuki-type contractions in the setting of topological vector space-valued cone metric space with a solid cone and establish some new fixed point results for multi-valued mappings. The problem of finding fixed points for multi-valued mappings satisfying locally contractive conditions on a closed ball is also addressed. Our findings generalize a number of well-established results in the literature. To highlight the uniqueness of our key finding, we present an example. As a demonstration of the applicability of our principal theorem, we prove a result in homotopy theory.

The aim of this research article is to explore the framework of tvs-cone b-metric spaces and establish some generalized common fixed point theorems for self mappings under generalized contractive conditions. To extend this theory, we introduce the notion of a generalized Hausdorff distance function in the framework of tvs-cone b-metric spaces and prove some novel fixed point results for multi-valued mappings. Our findings naturally encompass and generalize several known results in tvs-cone metric spaces, cone b-metric spaces, and cone metric spaces. To illustrate the applicability of the developed framework, we apply the main results to Fredholm integral 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.