Convergence theorems of the Ishikawa type iterative sequences with errors for generalized quasi-contractive mappings in convex metric spaces

AbstractIn this paper, some convergence theorems of Ishikawa type iterative sequence with errors for nonlinear generalized quasi-contractive mapping in convex metric spaces are proved. The results presented in this paper not only extend and improve the main results in [1–8] but also give an affirmative answer to the open question of Rhoades-Naimpally-Singh in convex metric spaces

Strong Convergence Theorem for Bregman Strongly Nonexpansive Mappings and Equilibrium Problems in Reflexive Banach Spaces

By using a new hybrid method, a strong convergence theorem for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of Bregman strongly nonexpansive mappings in a reflexive Banach space is proved

Some results for uniformly L -Lipschitzian mappings in Banach spaces

AbstractThe purpose of this work is to prove a strong convergence theorem for a pair of uniformly L-Lipschitzian mappings in Banach spaces. The results presented in the work improve and extend some recent results of Chang [S.S. Chang, Some results for asymptotically pseudo-contractive mappings and asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 129 (2001) 845–853], Cho et al [Y.J. Cho, J.I. Kang, H.Y. Zhou, Approximating common fixed points of asymptotically nonexpansive mappings, Bull. Korean Math. Soc. 42 (2005) 661–670], Ofoedu [E.U. Ofoedu, Strong convergence theorem for uniformly L-Lipschitzian asymptotically pseudocontractive mapping in a real Banach space, J. Math. Anal. Appl. 321 (2006) 722–728], Schu [J. Schu, Iterative construction of fixed point of asymptotically nonexpansive mappings, J. Math. Anal. Appl. 158 (1991) 407–413] and Zeng [L.C. Zeng, On the iterative approximation for asymptotically pseudo-contractive mappings in uniformly smooth Banach spaces, Chinese Math. Ann. 26 (2005) 283–290 (in Chinese); L.C. Zeng, On the approximation of fixed points for asymptotically nonexpansive mappings in Banach spaces, Acta Math. Sci. 23 (2003) 31–37 (in Chinese)]

Some results for uniformly L -Lipschitzian mappings in Banach spaces

AbstractThe purpose of this work is to prove a strong convergence theorem for a pair of uniformly L-Lipschitzian mappings in Banach spaces. The results presented in the work improve and extend some recent results of Chang [S.S. Chang, Some results for asymptotically pseudo-contractive mappings and asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 129 (2001) 845–853], Cho et al [Y.J. Cho, J.I. Kang, H.Y. Zhou, Approximating common fixed points of asymptotically nonexpansive mappings, Bull. Korean Math. Soc. 42 (2005) 661–670], Ofoedu [E.U. Ofoedu, Strong convergence theorem for uniformly L-Lipschitzian asymptotically pseudocontractive mapping in a real Banach space, J. Math. Anal. Appl. 321 (2006) 722–728], Schu [J. Schu, Iterative construction of fixed point of asymptotically nonexpansive mappings, J. Math. Anal. Appl. 158 (1991) 407–413] and Zeng [L.C. Zeng, On the iterative approximation for asymptotically pseudo-contractive mappings in uniformly smooth Banach spaces, Chinese Math. Ann. 26 (2005) 283–290 (in Chinese); L.C. Zeng, On the approximation of fixed points for asymptotically nonexpansive mappings in Banach spaces, Acta Math. Sci. 23 (2003) 31–37 (in Chinese)]

Some Results for a Finite Family of Uniformly -Lipschitzian Mappings in Banach Spaces

The purpose of this paper is to prove a strong convergence theorem for a finite family of uniformly L-Lipschitzian mappings in Banach spaces. The results presented in the paper not only correct some mistakes appeared in the paper by Ofoedu (2006) but also improve and extend some recent results by Chang (2001), Cho et al. (2005), Ofoedu (2006), Schu (1991), and Zeng (2003, 2005)

Coincidence point theorems for multivalued mappings

Some new coincidence point and fixed point theorems for multivalued mappings in complete metric space are proved. The results presented in this paper enrich and extend the corresponding results in [5-16, 20-25, 29]

Common fixed point theorems and applications

The purpose of this paper is to discuss the existence of common fixed points for mappings in general quasi-metric spaces. As applications, some common fixed point theorems for mappings in probabilistic quasi-metric spaces are given. The results presented in this paper generalize some recent results

Fixed point theorems in metric spaces and probabilistic metric spaces

In this paper, we prove some common fixed point theorems for compatible mappings of type (A) in metric spaces and probabilistic metric spaces Also, we extend Caristi's fixed point theorem and Ekeland's variational principle in metric spaces to probabilistic metric spaces