Approximating common solutions of variational inequalities by iterative algorithms with applications

In this paper, we introduce an iterative scheme for a general variational inequality. Strong convergence theorems of common solutions of two variational inequalities are established in a uniformly convex and 2-uniformly smooth Banach space. As applications, we, still in Banach spaces, consider the convex feasibility problem

Some Inequalities in 2-inner Product Spaces

In this paper we extend some results on the refinement of Cauchy-Buniakowski-Schwarz's inequality and Aćzel's inequality in inner product spaces to 2-inner product spaces

On Some Grüss Type Inequality in 2-Inner Product Spaces and Applications

In this paper, we shall give a generalization of the Grüss type inequality and obtain some applications of the Grüss type inequality in terms of 2-inner product spaces

Set-valued fixed-point theorems for generalized contractive mappings without the Hausdorff metric

AbstractIn this paper, the concept of a set-valued contractive mapping is considered by using the idea of a generalized distance, such as the τ-distance, in metric spaces without using the concept of the Hausdorff metric. Furthermore, under some mild conditions, we provide the existence theorems for fixed-point problems of the considered mapping. Hence, our results can be viewed as a generalization and improvement of many recent results

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)]

On some Gronwall type inequalities with iterated integrals

The main objective of the present paper is to establish some new Gronwall type inequalities involving iterated integrals