C -class functions and fixed point theorems for generalized α−η−ψ−φ−F− contraction type mappings in α−η− complete metric spaces

Abstract

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.

Some Common Fixed Point Results for Rational Contraction Type via the C-Class Functions on Metric Spaces

“…In this paper, we state some common fixed point theorems for rational contraction type via the C-class functions on metric spaces. The obtained results are generalizations of the main results in [1,12,14]. In addition, we study the existence of solutions to the system of nonlinear integral equations.…”

“…In 2016, Chuadchawna et al [6] improved and generalized the results in [12,14] by proving some fixed point theorems for α-η-ψ-Greraghty contraction type maps in α-η complete metric spaces. Recently, Ansari and Kaewcharoen [1] extended the results in [12] and proved the fixed point theorems for α-η-ψ-ϕ-F contraction type maps in α-η complete metric spaces by using the C-class function.…”

Common fixed points for pairs of triangular α-admissible mappings

“…In 2016, Ansari and Kaewcharoen [5] gave the definition of a generalized α − η − ψ − ϕ − F-contraction type mapping and proved same fixed point theorems for such mappings in complete metric spaces. Definition 1.5 ([5]).…”

“…Recently, Hussain et al [9] proved some fixed point results for single and multi-valued α − η − ψ-contractive type mapping in complete metric space. Very recently, Ansari and Kaewcharoen [5] introduced a new type of contraction based on α-admissible with respect to another function η and proved some fixed point theorems of such mappings.…”

Common Fixed Points for Mappings under Contractive Conditions of (α,β,ψ)-Admissibility Type

“…In meantime, Abdeljawad [24] expanded the notion of α-admissibility to a pair of functions. For some fixed point theorems on α-admissibility, we direct readers to read References [25][26][27][28][29][30][31].…”