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Absorbing maps and Fixed Point Theorem in Probabilistic Metric Spaces using implicit relation

Abhay S. Ranadive, Anuja Chouhan


Our goal is to estimate the population mean with an increased precision. Most common estimators used for the purpose are simple mean estimator, ratio estimator and product estimator. So several attempts has been made to achieve considerable gain in efficiency by modifying these estimators by employing transformations on both study variable and auxiliary variable. In the present paper a most general class of estimators of under unequal probability sampling (UPS) scheme is suggested and its large sample properties were studied. It is shown that the proposed class of estimators (optimum case) has greater precession than several competitive estimators.


Menger space, weakly compatible mappings, absorbing mapping, Semi-compatible mapping, reciprocal continuity.

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