International Journal of Difference Equations (IJDE). ISSN 0973-6069 Volume 19, Number 1 (2024), pp.35-45 © Research India Publications https://dx.doi.org/10.37622/IJDE/19.1.2024.35-45 Common Fixed-Point Theorems via A-Contraction and Implicit Relations in Parametric Metric Spaces Sheetal Yadav 1 , Manoj Ughade 2* , Shiva Verma 3 , and Manoj Kumar Shukla 4 1 Department of Mathematics, Mata Gujri Mahila Mahavidhyala (Auto), Jabalpur-482001, Madhya Pradesh, India 2,3,4 Department of Mathematics, Institute for Excellence in Higher Education (IEHE), Bhopal-462016, Madhya Pradesh, India Correspondence should be addressed to Manoj Ughade; manojhelpyou@gmail.com Abstract In this paper, we establish some common fixed-point theorems via A- contraction and implicit relations in complete parametric metric spaces. Our results extend and generalize some well-known results of Kannan [12], Bianchini [2], Reich [17], and Popa [16]. Keywords: fixed point theorem, parametric metric space, A-contraction, implicit relation. 2010 Mathematics Subject Classification: 47H10 INTRODUCTION In the field of science, fixed point theory and all of its applications have been popular topics. It is employed in several fields, including engineering, mathematical economics, mathematical biology, nonlinear analysis, and functional analysis. Frechet [7] developed the idea of a metric space. Then, a large number of mathematicians have investigated contractive maps' fixed points. The study of the existence and uniqueness of fixed points as well as common fixed points has been a prominent area of research since the establishment of the Banach contraction principle. In 1965, Zadeh [20] developed the idea of a fuzzy set. The concept of fuzzy metric space was first proposed by Kramosil and Michalek [14] in 1975. It is a generalization of statistical (probabilistic) metric space. An essential foundation for the development of fixed-point