Related Fixed Point Theorems via General Approach of Simulations Functions

Abstract

In this work, we extend and complement some results in view of general and wider structures, such as b−metric spaces. By considering existing classes of Ζ−contractions and Ψ−simulating functions with a solid impact in database results of fixed point theory, we introduce a new general class of simulating functions, called as Ψ−s simulation functions, and also types of κψ−s− contractions in a more general framework. This approach covers, extends, and unifies several published works in the early and late literature.

On Modified Interpolative Almost E−Type Contraction in Partial Modular b−Metric Spaces

“…Moreover, the notation of the simulation function has been generalized in many directions. For some of them, see [17][18][19][20][21][22][23][24].…”

Fixed Point Results for an Almost Generalized α -Admissible Z -Contraction in the Setting of Partially Ordered b-Metric Spaces

“…Due to its usefulness, Banach contraction principle has been extended and generalized in various spaces using different conditions either by modifying the basic contractive condition or by generalizing the ambient spaces or both. For some extensions of Banach contraction principle in metric spaces, see References [2][3][4][5][6][7][8][9][10][11][12].…”

“…Afterwards, Karapinar [25] originated the concept of α-admissible Z-contraction. For more works in this line of research, see References [3,4,9,12,25]. Recently, Melliani et al [9] introduced a new concept of α-admissible almost type Z-contraction and proved the existence of fixed points for admissible almost type Z-contractions in a complete metric space.…”