Common Fixed Point Theorem For Expansive Mappings In G-metric Spaces

Vats, Ramesh Kumar; Kumar, Sunil; Sihag, Vizender

doi:10.22436/jmcs.06.01.06

Cited by 3 publications

(4 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In 2010, Vats et al [26] introduced the concept of weakly compatible. Also, in 2010, Manro et al [17] introduced the concepts of weakly commuting, R-weakly commuting mappings, and R-weakly commuting mappings of type (P ), (A f ), and (A g ) in G-metric space.…”

Section: Lemma 17 ([1]mentioning

confidence: 99%

Common fixed point theorems for non-compatible self-maps in b-metric spaces

Zhong‐zhi¹,

Sadati²,

Sedghi³

et al. 2015

J. Nonlinear Sci. Appl.

View full text Add to dashboard Cite

By using R-weak commutativity of type (Ag) and non-compatible conditions of self-mapping pairs in b-metric space, without the conditions for the completeness of space and the continuity of mappings, we establish some new common fixed point theorems for two self-mappings. Our results differ from other already known results. An example is provided to support our new result. c 2015 All rights reserved.Keywords: b-metric space, common fixed point theorem, R-weakly commuting mappings of type (Ag), non-compatible mapping pairs. 2010 MSC: 47H10, 54H25.

show abstract

Section: Lemma 17 ([1]mentioning

confidence: 99%

Common fixed point theorems for non-compatible self-maps in b-metric spaces

Zhong‐zhi¹,

Sadati²,

Sedghi³

et al. 2015

J. Nonlinear Sci. Appl.

View full text Add to dashboard Cite

show abstract

“…Vats et al [46] introduced the concept of compatible and compatible mapping of type (A) in G-metric space and proved a common fixed point theorem for two pair of expansive mappings. Definition 57.…”

Section: Vats Kumar and Sihag (2013)mentioning

confidence: 99%

“…Definition 58. [46] Two self-mappings S and T of a G-metric space (X, G) are said to be compatible mappings of type (A) if…”

Section: Vats Kumar and Sihag (2013)mentioning

confidence: 99%

See 1 more Smart Citation

Advancements in Fixed Point Results of Generalized Metric Spaces: A Survey

Jiddah

Mohammed

Imam

2023

Sohag Journal of Sciences

View full text Add to dashboard Cite

The increasing significance of metric spaces and their applications in sciences and engineering has manifested over the years. This has led to the emergence of fixed point theory in metric spaces which in turn, has many practical usefulness in inequalities, approximation theory, optimization theory, image restoration and filtering, to mention but a few. Following up this development, in this paper, various results on G-metric spaces (also called generalized metric spaces) introduced by Mustafa and Sims are reviewed. Extensions of fixed point theorems for Lipschitzian-type mappings on G-metric spaces are compiled and a concise report on the transition in fixed point theorems on G-metric spaces are established. The aim of this survey is therefore, to examine and provide an up-to-date analysis of the important advancements in the fixed point theory of G-metric spaces. Consequently, this note is handy for researchers in the domain of metric and pseudo-metric spaces as they can easily appreciate how new results are delineated from the subsequent ones.

show abstract

Generalized Normed Spaces And Fixed Point Theorems

Khan¹

2014

J. Math. Computer Sci.

View full text Add to dashboard Cite

Gähler ([4], [5]) introduced and investigated the notion of 2-metric spaces and 2-normed spaces in sixties. These concepts are inspired by the notion of area in two dimensional Euclidean space. In this paper, we choose a fundamentally different approach and introduce a possible generalization of usual norm retaining the distance analogue properties. This generalized norm will be called as -norm. We show that every G-normed space is a G-metric space and therefore, a topological space and develop the theory for G-normed spaces. We also introduce G-Banach spaces and obtain some fixed point theorems.

show abstract

Common Fixed Point Theorem For Expansive Mappings In G-metric Spaces

Cited by 3 publications

References 4 publications

Common fixed point theorems for non-compatible self-maps in b-metric spaces

Common fixed point theorems for non-compatible self-maps in b-metric spaces

Advancements in Fixed Point Results of Generalized Metric Spaces: A Survey

Generalized Normed Spaces And Fixed Point Theorems

Contact Info

Product

Resources

About