Fixed Point Theorems in Cone Banach Spaces


In this manuscript, a class of self-mappings on cone Banach spaces which have at least one fixed point is considered. More precisely, for a closed and convex subset C of a cone Banach space with the norm ‖x‖P dx, 0, if there exist a, b, s and T: C → C satisfies the conditions 0 ≤ s |a | −2b < 2a b and 4adTx, Ty bdx, Tx dy, Ty ≤ sdx, y for all x, y ∈ C, then T has at least one Fixed point

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