A new extension of Kannan contractions and related fixed point results

A Common Fixed Point Theorem for Generalised F -Kannan Mapping in Metric Space with Applications

“…Remark 9 (see [28]). By properties of F, it follows that every F-Kannan mapping T on a metric space ðX, dÞ satisfies the following condition:…”

“…In 2019, Goswami et al [22] defined F-contractive type mappings in b-metric spaces and proved some fixed point results with suitable examples. Recently, Batra et al [28] noticed that the definition introduced by Goswami et al [22] is not meaningful in general. They provided suitable examples to support their opinion on this definition.…”

“…They provided suitable examples to support their opinion on this definition. Therefore, Batra et al [28] gave the notions of F-contraction and Kannan mapping to define a new class of contractions called F-Kannan mappings which is in true sense a generalization of Kannan mappings.…”

“…Motivated by Batra et al [28], we use the following notations: Let X be a nonempty set and ðX, dÞ denotes the metric space with metric d. Define the cardinality of a set A by card fAg and FixT denotes the set of all fixed points of a mapping T.…”

“…Batra et al [28] gave a new generalization family of contraction called F-Kannan mapping and introduced the following definition. Definition 8 (see [28]). Let F be a mapping satisfying (F1)-(F3).…”