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In this paper, we extend the well-known definitions of \(\alpha \) -admissible and \((\alpha ,\beta )\) -admissible and introduce new definitions of \((\alpha _{qs^p},\beta _{qs^p})\) -admissible, \((\alpha _{qs^p},\beta _{qs^p})\) -orbital admissible, triangular \((\alpha _{qs^p},\beta _{qs^p})\) -orbital admissible. With these new definitions we introduce a new hybrid contraction which we named as \((\alpha _{qs^p},\beta _{qs^p}){-}\phi \) -hybrid contraction. With the help of this new contraction we prove some fixed point theorems in b-metric spaces. Further, we study the general Ulam-type stability and well-posedness for the newly introduced hybrid contraction.

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On Fixed Points of  \((\alpha _{qs^p}, \beta _{qs^p})\!{-}\!\phi -\) Hybrid Contraction in  \(b-\) Metric Spaces

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  • 发表日期：

    2026年

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  • Loitongbam Melei Singh,
  • Yumnam Rohen

摘要

In this paper, we extend the well-known definitions of \(\alpha \) -admissible and \((\alpha ,\beta )\) -admissible and introduce new definitions of \((\alpha _{qs^p},\beta _{qs^p})\) -admissible, \((\alpha _{qs^p},\beta _{qs^p})\) -orbital admissible, triangular \((\alpha _{qs^p},\beta _{qs^p})\) -orbital admissible. With these new definitions we introduce a new hybrid contraction which we named as \((\alpha _{qs^p},\beta _{qs^p}){-}\phi \) -hybrid contraction. With the help of this new contraction we prove some fixed point theorems in b-metric spaces. Further, we study the general Ulam-type stability and well-posedness for the newly introduced hybrid contraction.