In this paper, we obtain some fixed point results for generalized weakly contractive mappings with some auxiliary functions in the framework of b-metric spaces. The proved results generalize and extend the corresponding well-known results of the literature. Some examples are also provided in order to show that these results are more general than the well-known results existing in literature. MSC: Primary 47H10; secondary 54H25

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 concept of generalized α-η-ψ-ϕ-F -contraction type mappings where ψ is the altering distance function and ϕ is the ultra altering distance function. The unique fixed point theorems for such mappings in the setting of α-η-complete metric spaces are proven. We also assure the fixed point theorems in partially ordered metric spaces. Moreover, the solution of the integral equation is obtained using our main result.

The aim of this paper is to introduce the notions of α-(F , H)-ϕ, ψ and µ-(F , H)-ϕ, ψ contractions and present several coupled fixed point theorems for this type of contractions in the set of ordered metric spaces. Several examples are offered to illustrate the validity of the obtained results. As an application, the existence of a solution of Fredholm nonlinear integral equations are also investigated.

In this paper, we introduced the concepts pair (F , h) a upclass of type II and α β -contractive mappings and show that theorems in [4]reduce to corollaries in this paper. that is, all them can obtain of one theorem. in end we state example for support main result.