Abstract
A foremost general contraction condition is introduced to prove the existence of fixed points for a self-mapping in a complete metric space whose orbital diametral functions are closed. This condition covers not only the Kannan type but also covers Reich, and Hardy and Roger's type contractive conditions. An example is given in its support.
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G. E. Hardy and T. D. Rogers, A generalization of a fixed point theorem of Reich, Canad. Math. Bull. 16 (1973), 201–206.
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R. Kannan, Some results on fixed point, Bull. Calcutta Math. Soc., 60 (1968), 71–76.
S. Reich, Some remark's concerning contraction mappings, Canad. Math. Bull., 14 (1971), 121–124.
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Communicated by Ding Xieping
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Sharma, B.K., Thakur, B.S. Fixed point with orbital diametral function. Appl Math Mech 17, 145–148 (1996). https://doi.org/10.1007/BF00122309
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DOI: https://doi.org/10.1007/BF00122309