In this paper, we present some sufficient conditions for which a Banach space has normal structure and therefore the fixed point property for nonexpansive mappings in terms of the generalized James, von Neumann-Jordan, Zbȃganu constants, the Ptolemy constant and the Domínguez-Benavides coefficient. Our main results extend and improve some known results in the recent literature.
Recently, Cui and Lu have introduced the constant H p (X) (p ∈ R) of a Banach space X by using Hölder's means. In this paper, we determine and estimate the new constant under the absolute normalized norms on R 2 by means of their corresponding continuous convex functions on [0, 1]. Furthermore, the exact values of the constant are calculated in some concrete Banach spaces. In particular, we calculate the precise values of the constants A 2 (X) and T(X) and the Gao constant E(X) in these concrete spaces.
In this paper, we introduce the concept of (ψ, ϕ) s -weakly C-contractive mappings in the setup of partially ordered b-metric spaces and investigate some fixed point and common fixed point results for such wmappings. Our main results generalize several well-known comparable results in the recent literature. Furthermore, we furnish some suitable examples and an applications of a common solution for a system of integral equations to illustrate the effectiveness and usability of our obtained results.
In this paper, we show some geometric conditions on Banach spaces by considering Hölder's means and many well known parameters namely the James constant, the von Neumann-Jordan constant, the weakly convergent sequence coefficient, the normal structure coefficient, the coefficient of weak orthogonality, which imply the existence of fixed points for multivalued nonexpansive mappings and normal structure of Banach spaces. Some of our main results improve and generalize several known results in the recent literature on this topic. We also show that some of our results are sharp.
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