In this paper, we establish some new fixed point theorems for generalized ϕ–ψ-contractive mappings satisfying an admissibility-type condition in a Hausdorff rectangular metric space with the help of C-functions. In this process, we rectify the proof of Theorem 3.2 due to Budhia et al. [New fixed point results in rectangular metric space and application to fractional calculus, Tbil. Math. J., 10(1):91–104, 2017]. Some examples are given to illustrate the theorems. Finally, we apply our result (Corollary 3.6) to establish the existence of a solution for an initial value problem of a fractional-order functional differential equation with infinite delay.

In this paper, we introduce the two new concepts of an α-type almost-F-contraction and an α-type F Suzuki contraction and prove some fixed point theorems for such mappings in a complete metric space. Some examples and an application to a nonlinear fractional differential equation are given to illustrate the usability of the new theory. MSC: 47H10; 54H25; 37C25

In this paper, we introduce α − ψ type contractive mapping in rectangular metric space satisfying certain admissibility conditions and prove a fixed point result for such mapping in complete and Hausdorff rectangular metric space. Some examples are given to justify our result. Also we have shown that the existence of solution of a nonlinear fractional differential equation can be guaranteed, as an application of our result.