Fixed Point Theorems for Kannan Interpolative, Riech Interpolative and Dass-Gupta Interpolative Rational type Contractions in A-Metric Spaces
Sheetal Yadav *
Department of Mathematics, Mata Gujri Mahila Mahavidhyala (Auto), Jabalpur-482001, Madhya Pradesh, India.
Manoj Ughade
Department of Mathematics, Institute for Excellence in Higher Education (IEHE), Bhopal-462016, Madhya Pradesh, India.
Deepak Singh Singh
Department of Mathematics, Swami Vivekanand University, Sagar-470001, Madhya Pradesh, India.
Manoj Kumar Shukla
Department of Mathematics, Institute for Excellence in Higher Education (IEHE), Bhopal-462016, Madhya Pradesh, India.
*Author to whom correspondence should be addressed.
Abstract
(\(\lambda\), \(\alpha\))- interpolative Kannan contraction, (\(\lambda\), \(\alpha\), \(\beta\))- interpolative Kannan contraction, (\(\lambda\), \(\alpha\), \(\beta\), \(\gamma\))- interpolative Riech contraction and (\(\lambda\), \(\alpha\), \(\beta\))- interpolative Dass-Gupta rational contraction are presented in this study. Furthermore, we prove a few fixed-point theorems for interpolative contractions in complete A-metric spaces. These theorems also extend and apply to an A-metric setting several interesting results from metric fixed-point theory.
Keywords: fixed-point, interpolative contraction, A-metric spaces