In 1962, Gallagher proved a higher-dimensional version of Khintchine’s theorem on Diophantine approximation. Gallagher’s states that for any non-increasing approximation function ψ: ℕ → (0, 1/2) with $$\sum\nolimits_{q = 1}^\infty {\psi \left( q \right)} $$ and γ γ′ 0 the following set $$\left\{ {\left( {x,y} \right) \in {{\left[ {0,\,1} \right]}^2}:\left\| {qx - \gamma } \right\|\left\| {qy {\...

in this paper is introduced a new type of generalization of metric spaces called sb metric space. for this new kind of spaces it has been proved a common xed point theorem for four mappings which satisfy generalized contractive condition. we also present example to con rm our theorem.

recently, phiangsungnoen et al. [j. inequal. appl. 2014:201 (2014)] studied fuzzy mappings in the framework of hausdorff fuzzy metric spaces.following this direction of research, we establish the existence of fixed fuzzy points of fuzzy mappings. an example is given to support the result proved herein; we also present a coincidence and common fuzzy point result. finally, as an application of ou...

in this paper the bagley-torvik equation as a prototype fractional differential equation with two derivatives is investigated by means of homotopy perturbation method. the results reveal that the present method is very effective and accurate.

in this paper, we prove the existence of fixed point for chatterjea type mappings under $c$-distance in cone metric spaces endowed with a graph. the main results extend, generalized and unified some fixed point theorems on $c$-distance in metric and cone metric spaces.

in this paper, we give some results on the common fixed point of self-mappings defined on complete $b$-metric spaces. our results generalize kannan and chatterjea fixed point theorems on complete $b$-metric spaces. in particular, we show that two self-mappings satisfying a contraction type inequality have a unique common fixed point. we also give some examples to illustrate the given results.

A player moving in the plane is given a sequence of instructions of the following type: at step i a planar convex set Fi is specified, and the player has to move to a point in Fi. The player is charged for the distance traveled. We provide a strategy for the player which is competitive, i.e., for any sequence Fi the cost to the player is within a constant (multiplicative) factor of the "off-lin...