In this manuscript, we introduce a new hybrid contraction that unify several nonlinear and linear contractions in the set-up of a complete metric space. We present an example to indicate the genuine of the proved result. In addition, we consider Ulam type stability and well-posedness for this new hybrid contraction.
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In this paper we prove a coincidence theorem by generalizing the diverse coincidence theorems and fixed point theorems of Baillon - Singh [1], Czerwik [5], Singh Gairola [22], Kaneko [9], Kaneko - Sessa [10], Reddy-Subrahmanyam [16] and others for a system of single-valued and multi-valued maps by introducing the concept of coordinatewise R-weakly commuting maps inspired by Pant [15].
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