Paired-Chatterjea type contractions: Novel fixed point results and continuity properties in metric spaces
Abstract
Introduction/purpose: The paper deals with Paired-Chatterjea type contraction mappings as an extension of traditional Chatterjea type contractions that operates on three points rather than two, in the framework of standard metric spaces.
Methods: The concept of Chatterjea type contraction mappings is employed in a metric space on three points rather than two using the idea of paired contraction mappings.
Results: A series of corresponding properties has been discussed. Furthermore, it is established that Paired-Chatterjea type mappings form a distinct class from traditional Chatterjea type mappings and obtain at least one fixed point in the absence periodic points of prime period 2 within complete metric spaces. It is also demonstrated that how additional criteria to these mappings, such as continuity and asymptotic regularity, broaden the scope of fixed point results. Extending beyond Chatterjea’s foundational contributions, two additional fixed point results applicable to Paired-Chatterjea type mappings in metric spaces are established, even in scenarios where completeness is not required.
Conclusions: Paired-Chatterjea type mappings are generally discontinuous; they exhibit continuity at fixed points similar to Kannan and Chatterjea type mappings. In the absence of a periodic point of prime period 2, these mappings have a fixed point within the complete metric space.
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