Mathematics and Statistics Vol. 11(2), pp. 340 - 344
DOI: 10.13189/ms.2023.110213
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m-Continuity and Fixed Points in -Complete G-Metric Spaces

Banoth Madanlal Naik ^*, V.Naga Raju
University College of Science, Osmania University, India

ABSTRACT

Fixed point technique can be considered as one of the most powerful tools to solve problems which occur in several fields like Physics, Chemistry, Computer Science, Economics and other subbranches of Mathematics etc. Banach [3] gave the first result in the field of metric fixed point theory which guarantees the existence and uniqueness of a fixed point in a complete metric space. Thereafter, many Mathematicians replace the notion of metric space and Banach contractive condition with various generalized metric spaces and different contractions to prove fixed point theorems. One such generalized metric space, called G-metric space, was proposed in [6]. Abhijit Pant, R.P.Pant [1] introduced a new type of contraction and obtained some results in metric spaces in the year 2017. The purpose of this paper is to define -complete G-metric space and study three metric fixed point results for such spaces. In the first two fixed point results, we use weaker form of continuity, called m-continuity and new type contractive conditions while in the third result simulation function is used. The results which we obtained will improve, extend and generalize some results in [1] and [2] in the existing literature. In addition to this, we give examples to validate our results.

KEYWORDS
G-metric Space, m-continuity, -set, -complete, Simulation Function

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Banoth Madanlal Naik , V.Naga Raju , "m-Continuity and Fixed Points in -Complete G-Metric Spaces," Mathematics and Statistics, Vol. 11, No. 2, pp. 340 - 344, 2023. DOI: 10.13189/ms.2023.110213.

(b). APA Format:
Banoth Madanlal Naik , V.Naga Raju (2023). m-Continuity and Fixed Points in -Complete G-Metric Spaces. Mathematics and Statistics, 11(2), 340 - 344. DOI: 10.13189/ms.2023.110213.