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This paper introduce a new class of operators and contraction mapping for a cyclical map T on G-metric spaces and the approximately fixed point properties. Also,we prove two general lemmas regarding approximate fixed Point of cyclical contraction mapping on G-metric spaces. Using these results we prove several approximate fixed point theorems for a new class of operators on G-metric spaces (not necessarily complete). These results can be exploited to establish new approximate fixed point theorems for cyclical contraction maps. Further,there is a new class of cyclical operators and contraction mapping on G-metric space (not necessarily complete)which do not need to be continuous.Finally,examples are given to support the usability of our results.
In this paper, we prove some common coupled fixed point theorems for mappings satisfying different contractive conditions in the context of complete $C^*$-algebra-valued metric spaces. Moreover, the paper provides an application to prove the existenc
In this paper, we first define the concept of convexity in G-metric spaces. We then use Mann iterative process in this newly defined convex G-metric space to prove some convergence results for some classes of mappings. In this way, we can extend seve
We study approximately differentiable functions on metric measure spaces admitting a Cheeger differentiable structure. The main result is a Whitney-type characterization of approximately differentiable functions in this setting. As an application, we
In this paper, we construct a homeomorphism on the unit closed disk to show that an invertible mapping on a compact metric space is Li-Yorke chaotic does not imply its inverse being Li-Yorke chaotic.
In this paper, we establish two gap theorems for ends of smooth metric measure space $(M^n, g,e^{-f}dv)$ with the Bakry-Emery Ricci tensor $mathrm{Ric}_fge-(n-1)$ in a geodesic ball $B_o(R)$ with radius $R$ and center $oin M^n$. When $mathrm{Ric}_fge