Multivalued Extensions of Krasnosel’skii-Type Fixed-Point Theorems in p-Normed Spaces
Keywords:
p-normed space, Fixed-point theorem, Contraction operator, Multivalued operator, Measure of noncompactness, Darbo–Sadovski theorem, Krasnosel’skii theorem, Nonlinear integral equation, s-convexity, Existence results, Numerical applicationsAbstract
This paper establishes new fixed-point theorems in the framework of complete p-normed spaces, where p ∈ (0, 1]. By extending the classical Banach, Schauder, and Krasnosel’skii fixed-point theorems, we derive several results for the sum of contraction and compact operators acting on s-convex subsets. The analysis is further generalized to multivalued upper semi-continuous operators by employing Kuratowski and Hausdorff measures of noncompactness. These results lead to new Darbo–Sadovskii-type fixed-point theorems and global versions of Krasnosel’skii’s theorem for multifunctions in p-normed spaces. The theoretical findings are then applied to demonstrate the existence of solutions for nonlinear integral equations formulated in p-normed settings. A section on numerical applications is also provided to illustrate the effectiveness and applicability of the proposed results.
