In the present paper, we prove some fixed point theorems by using non-decreasing mapping \(\kappa :\mathbb{R}^+\to \mathbb{R}^+\) known as altering distance function or control function, in context of \(S\)-metric space. Further, explore property \(P\) for these contractive mappings.

Using Cesàro means of a mapping, we modify the progress of Mann’s iteration in hybrid method for asymptotically nonexpansive mappings in Hilbert spaces. Under suitable conditions, we prove that the iterative sequence converges strongly to a fixed point of an asymptotically nonexpansive mapping. We also introduce a new hybrid iterative scheme for finding a common element of the set of common fix...

In this paper, we give (?,?)-weak Pata contractive mapping by using the simulation function and multivalued contractions establish some fixed point results for such contractions. Also, an example related to mappings via function. Our generalize Pata-type Banach Consequently, obtained encompass several in literature.

In this paper, we obtain the results of coincidence and common fixed points in b-metric spaces. We work with a new type multivalued quasi-contractive mapping nonlinear comparison functions. Our generalize improve several recent results. Additionally, give an application obtained to dynamical systems.