In this paper, we prove the existence of solutions for a variational-like inequality and a generalized variational-like inequality in the relaxed η-α pseudomonotone and strictly η-quasimonotone cases in Banach spaces by using the KKM technique. The results presented in this paper improve and extend some corresponding results of several authors. [ABSTRACT FROM AUTHOR]
The purpose of this paper is to introduce the concepts of total asymptotically demicontractive mappings and total asymptotically hemicontractive mappings. Under suitable conditions some strong convergence theorems for these two kinds of mappings to converge to their fixed points in CAT(0) space are proved. The results presented in the paper extend and improve some recent results announced in the current literature. [ABSTRACT FROM AUTHOR]
In this paper, we study an operator version of the modified Browder-Tikhonov regularization method for finding a common solution for a system of ill-posed operator equations involving m-accretive operators Ai, i = 0, ... ,N, in a reflexive Banach space. The convergence rates of the regularized solutions are estimated not only in the infinite-dimensional space, but also in connection with its finite-dimensional approximations without the weakly sequential continuity of the dual mapping. [ABSTRACT FROM AUTHOR]
In this work, we introduce the class of α-ψ-Geraghty contraction as well as generalized α-ψ-Geraghty contraction mappings in the context of generalized metric spaces where ψ is an auxiliary function which does not require the subadditive property and set up some fixed point results for both classes individually. Our results will extend, improve and generalize several existing results in the literature. [ABSTRACT FROM AUTHOR]