Sentence examples for mappings which generalizes from inspiring English sources
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].
By using the idea of Caristi's fixed point theorem [2], Chuang et al. [3] proved a unique fixed point theorem for single-valued mappings which generalizes Theorem 1.1.
In 1969, Takahashi [3] proved the first fixed point theorem for a noncommutative semigroup of nonexpansive mappings which generalizes De Marr's fixed point theorem [4].
We established another generalization of the Ostrowski-Grüss type inequality using the weighted Grüss inequality for bounded differentiable mappings which generalizes the previous inequalities developed and discussed in [3 5].
Later on, Kirk and Xu [23] introduced the concept of asymptotic pointwise nonexpansive mappings which generalizes the concept of asymptotically nonexpansive mappings and proved the existence of fixed points for such maps in a uniformly convex Banach space.
In this paper, we establish another generalization of the Ostrowski-Grüss type inequality using the weighted Grüss inequality for bounded differentiable mappings which generalizes the previous inequalities developed and discussed in [3 5].
Recently, Imdad and Soliman [15] introduced fixed point theorems for an asymptotically regular semigroup of uniformly generalized Lipschitzian mappings which generalize the results due to Jen-Chih Yao and Lu-Chuan Zeng [14].
Recently, Beg et al. [29] considered a general class of random mappings which generalize the contractive operators due to Osilike [32], Imoru and Olatinwo [33], and Bosede and Rhoades [34] in a stochastic version.
In 2008 Suzuki [1] introduced a new type of mappings which generalize the well-known Banach contraction principle [2].
Very recently, Lan et al. [16] introduced a new concept of ( A, η ) -accretive mappings, which generalized the existing monotone or accretive operators, and studied some properties of mappings.
In this section, using means and w-distances, we first prove an existence theorem for mappings in metric spaces which generalizes Takahashi et al. [7].
