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This chapter presents common fixed point theorems for absorbing mappings that satisfy a generalized \(\phi \) -weak contraction involving cubic terms of distance function. Present results are useful in two ways. Firstly, by using the notion of both compatibility and pointwise absorbing mappings, it widens the area of the study of common fixed point theorems from the class of compatible mapping to the wider class of pointwise absorbing mapping. Secondly, our theorem does not force the mappings to be continuous even at the common fixed point. At the end, we show that pointwise absorbing mapping is a necessary condition for the existence of common fixed point of mapping pairs in metric space.

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Fixed Points for Absorbing Mappings Satisfying a Generalized \(\phi \) -Weak Contraction Condition that Involves Cubic Terms of Distance Function

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  • 发表日期：

    2025年

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  • Sanjay Kumar,
  • Rajesh Kumar,
  • Choonkil Park

摘要

This chapter presents common fixed point theorems for absorbing mappings that satisfy a generalized \(\phi \) -weak contraction involving cubic terms of distance function. Present results are useful in two ways. Firstly, by using the notion of both compatibility and pointwise absorbing mappings, it widens the area of the study of common fixed point theorems from the class of compatible mapping to the wider class of pointwise absorbing mapping. Secondly, our theorem does not force the mappings to be continuous even at the common fixed point. At the end, we show that pointwise absorbing mapping is a necessary condition for the existence of common fixed point of mapping pairs in metric space.