for fr$acute{mathbf{text{e}}}$chet algebras $(a, (p_n))$ and $(b, (q_n))$, a linear map $t:arightarrow b$ is textit{almost multiplicative} with respect to $(p_n)$ and $(q_n)$, if there exists $varepsilongeq 0$ such that $q_n(tab - ta tb)leq varepsilon p_n(a) p_n(b),$ for all $n in mathbb{n}$, $a, b in a$, and it is called textit{weakly almost multiplicative} with respect to $(p_n)$ and $(q_n)$,...

In this paper, first we prove common fixed point theorems for a pair of weakly compatible maps. Secondly, we prove a fixed point theorem for weakly compatible maps along with (CLRg) property. In fact, our results generalize the results of Z. Mustafa et al. [10]. 2000 AMS Classification: 47H10, 54H25

We prove a unique common fixed-point theorem for two pair of weakly compatible maps in a complete metric space, which generalizes the result of Brian Fisher by a weaker condition such as weakly compatibility instead of compatibility and contractive modulus instead of continuity of maps.

We construct SRB measures for endomorphisms satisfying conditions far weaker than the usual non-uniform expansion. As a consequence, the definition of a non-uniformly expanding map can be weakened. We also prove the existence of an absolutely continuous invariant measure for local diffeomorphisms, only assuming the existence of hyperbolic times for Lebesgue almost every point in the manifold.

Object localization is an important computer vision problem with a variety of applications. The lack of large scale object-level annotations and the relative abundance of image-level labels makes a compelling case for weak supervision in the object localization task. Deep Convolutional Neural Networks are a class of state-of-the-art methods for the related problem of object recognition. In this...

The object of this paper is to establish a theorem for a unique common fixed point of four self mappings, weakly compatibile in pairs and satisfying a generalized contractive condition in a cone metric space. Our result generalizes and synthesizes the results of Abbas– Jungck [1], Arshad et al. [2], Huang–Zhang [3] and Vetro [8].