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Abstract
A number of generalized metric spaces have been defined or characterized in terms of g-functions. Symmetric g-functions are discussed by C. Good, D. Jennings and A. M. Mohamad. In this paper, some questions about symmetric g-functions are answered, particularly it is shown that every sym-wg-space is expandable.
Abstract
We prove expansion mappings theorems in various spaces i.e., metric spaces, generalized metric spaces, probabilistic metric spaces and fuzzy metric spaces, which generalize the results of various authors like Daffer and Kaneko [11], Ahmad, Ashraf and Rhoades [1], Vasuki [38], Rhoades [31] and Wang, Li, Gao and Iseki [40] etc.
] C . Good , M . Sergio . Symmetric products of generalized metric spaces . Topol. Appl ., 206 : 93 – 114 , 2016 . [8
In this paper several fixed point theorems for a class of mappings defined on a complete G-metric space are proved. In the same time we show that if the G-metric space (X, G) is symmetric then the existence and uniqueness of these fixed point results follows from the Hardy-Rogers theorem in the induced usual metric space (X, d G). We also prove fixed point results for mapping on a G-metric space (X, G) by using the Hardy-Rogers theorem where (X, G) need not be symmetric.
://auburn.edu/~gruengf/papers/dsurv7.pdf . [13] Gruenahge , G. 1984 Generalized metric spaces Kunen , K. , Vaughan , J. E. (eds.) Handbook of Set-Theoretic Topology
, Topology Appl. , 159 ( 2012 ), 1415 – 1420 . [17] Liu , C. and Lin , S. , Generalized metric spaces with algebraic structures , Topology
45 ( 2012 ), 1180 – 1187 . doi: 10.1016/j.chaos.2012.05.003 . [17] Good , C. , and Macias , S . Symmetric products of generalized metric spaces . Topology and its Applications 206 ( 2016 ), 93 – 114 . doi: 10.1016/j.topol.2016.03.019 . [18
