Department of Mathematics
URI for this collectionhttps://rps.wku.edu.et/handle/123456789/45781
Department of Mathematics
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Item COMMON BEST PROXIMITY POINT RESULTS FOR MULTI-VALUED CYCLIC MAPPINGS ON PARTIAL METRIC SPACES(wolkite University, 2025-02-28) AZIZEW ABATEThis thesis investigates best proximity point theory as a natural generalization of classical fixed point results to non-self mappings. The study focuses on generalized (α,T)-contraction mappings, cyclic and multi-valued in partial metric spaces. By unifying concepts from Hausdorff metric space and partial metric spaces, we develop existence and uniqueness theorems for best proximity points under various contractive conditions. The results extend the principle to provide new insights into cyclic and multi-valued mappings. Illustrative examples are presented to verify the applicability of the findingsItem BEST PROXIMITY THEOREM FOR GENERALIZED (θ, γ)-PROXIMAL CONTRACTION MAPPING IN RECTANGULAR QUASI B- METRIC SPACE(Wolkite University, 2025-01-10) KASAHUN BEYENE BEJIGAThis paper explores best proximity point theorems whit in the framework of broad (θ,γ) proximal reduction “mappings in rectangular quasi b-metric spaces”. “We introduce the class of rectangular quasi b- metric” space as a broadening of rectangular metric space, “rectangular quasi” b-metric space, “rectangular b-metric” space,define broad (θ,γ)proximal reduction mappings. Establish situation under which a optimal proximity point exists and provide example to clear my results. Extend previous work on fixed point theorems and contribute to the theory of proximity points in non-standard metric spaces.Item BEST PROXIMITY THEOREM FOR GENERALIZED (θ,γ)-PROXIMAL CONTRACTION MAPPING IN RECTANGULAR QUASI B- METRIC SPACE(WOLKITE UNIVERSITY, 2025-06-10) KASAHUN BEYENE BEJIGAThis paper explores best proximity point theorems whit in the framework of broad (θ,γ) proximal reduction “mappings in rectangular quasi b-metric spaces”. “We introduce the class of rectangular quasi b- metric” space as a broadening of rectangular metric space, “rectangular quasi” b-metric space, “rectangular b-metric” space,define broad (θ,γ)proximal reduction mappings. Establish situation under which a optimal proximity point exists and provide example to clear my results. Extend previous work on fixed point theorems and contribute to the theory of proximity points in non-standard metric spaces.