In this paper, we first introduce the concept of TVS-cone b-metric space which generalize the concept of b-metric space and cone b-metric space.
We define the concept of the generalized -concave operators, which generalize the definition of the -concave operators.
In this paper, we introduce a new type of metric spaces which generalize the concepts of metric spaces and operator-valued metric spaces, and give some related fixed point theorems for self-maps with contractive or expansive conditions on such spaces.
We study distributions which generalize the concept of spectral shift function, for pseudo-differential operators on Rd.
We introduce the relative oscillation numbers which generalize the concept of a weighted zero of the Wronskian for the matrix case.
Subsequently, Xin and Jiang [19] introduced noncommutative Banach spaces which generalize the concept of Banach spaces and established fixed point theorems for mappings with the k-ordered contractive condition.
In the paper, we introduce noncommutative Banach spaces which generalize the concept of Banach spaces, and the k-ordered contractive condition; we then discuss an ordered structure and several properties on noncommutative Banach spaces.
In details, we firstly introduce the concept of generalized k-ordered contractions in noncommutative Banach spaces, and prove some common fixed point theorems for generalized k-ordered contractions which generalize the results in [19] (see Theorem 2.1).
In this paper, using the concept of w-distances, and we prove existence theorems for single-valued mappings and set-valued mappings in a complete metric space which generalize Takahashi, Wong, and Yao's theorems.
On the other hand, Verma [4, 5] introduced the concept of -monotone mappings, which generalizes the well-known general class of maximal monotone mappings and originates way back from an earlier work of the Verma [7].
