The existence of fixed point in orthogonal metric spaces has been initiated by Eshaghi and et. al [7]. In this paper, we prove existence and uniqueness theorem of fixed point for mappings on $varepsilon$-connected orthogonal metric space. As a consequence of this, we obtain the existence and uniqueness of fixed point for analytic function of one complex variable. The paper concludes with some i...

Recently, authors [2] have discussed some equivalent relations for ρ-uniform stabilities of a given equation and those of its limiting equations by using the skew product flow constructed by quasi-processes on a general metric space. In 1992, Murakami and Yoshizawa [6] pointed out that for functional differential equations with infinite delay on a fading memory space B = B((−∞, 0];R) ρ-stabilit...

Diophantine approximation is traditionally the study of how well real numbers are approximated by rationals. We propose a model for studying in an arbitrary totally bounded metric space where rationals replaced with countable hierarchy “well-spread” points, which we refer to as abstract prove various Jarník–Besicovitch type dimension bounds and investigate their sharpness.

The xed point result in Mustafa-Sims metrical structures obtained by Karapinar and Agarwal[Fixed Point Th. Appl., 2013, 2013:154] is deductible from a corresponding one stated in terms ofanticipative contractions over the associated (standard) metric space.