Abstract
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.
Highlights
Fixed point theory is a very popular tool in solving existence problems in many branches of Mathematical Analysis and its applications
In physics and engineering fixed point technique has been used in areas like image retrieval, signal processing and the study of existence and uniqueness of solutions for a class of nonlinear integral equations
In 1968, Kannan proved a fixed point theorem for operators which need not be continuous
Summary
Fixed point theory is a very popular tool in solving existence problems in many branches of Mathematical Analysis and its applications. In 1968, Kannan (see [7] ) proved a fixed point theorem for operators which need not be continuous. In 1972, by combining the above three independent contraction conditions above, Zamfirescu (see [22]) obtained another fixed point result for operators which satisfy the following. In 2006, Berinde (see [4]) obtained some result on α−contraction for approximate fixed point in metric space. Miandaragh et al [9, 10] obtained some result on approximate fixed points in metric space. Mohsenalhosseini in [14] introduced the approximate fixed point in G-metric spaces for various types of operators. In 2017 Mohsenialhosseini [15] introduced the approximate fixed points of operators on G-metric spaces. We give some illustrative example of our main results
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