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In this paper, we obtain a new convergence theorem for fixed points of weak contractions in Branciari type generalized metric spaces under weaker conditions. The proof process of the theorem is new and different from that of other authors. An illustrative example of this theorem is to show how the new conditions extend known results.

In this paper, we study the existence and uniqueness of fixed points for generalized weak contractions under some proper assumptions. Our theorems include the known results of [1]-[6].

In this paper, we establish a convergence theorem for fixed points of generalised weak contractions in complete metric spaces under some new control conditions on the functions. An illustrative example of a generalised weak contraction is discussed to show how the new conditions extend known results.

Let E be an arbitrary uniformly smooth real Banach space, D be a nonempty closed convex subset of E ,a ndT : D → D a generalized Lipschitz Φ-contractive mapping with q ∈ F(T) � /

We prove the equivalence of the convergence of the Mann and Ishikawa iterations with errors for uniformly continuous generalized Φ-pseudocontractive mappings in normed linear spaces. Our results extend and improve the corresponding results of Xu, 1998, Kim et al., 2009, Ofoedu, 2006, Chidume and Zegeye, 2004, Chidume, 2001, Chang et al. 2002, Liu, 1995, Hirano and huang, 2003, C. E. Chidume and C. O. Chidume, 2005, and huang, 2007.

In this paper, the equivalence of the convergence among Mann-Ishikawa and Noor iterations is obtained for uniformly L-Lipschitzian mappings in real Banach spaces. Our results extend and improve the corresponding results in Chang (3) and Ofoedu (4).

In this paper, the proofs of theorem concerning Rafiq [Arif Rafiq, Modified Noor iterations for nonlinear equations in Banach spaces, Appl. Math. Comput. 182 (2006) 589–595] are proved incorrect. And his results are revised.

In this paper, we prove that the equivalence between the convergence of Mann and Ishikawa iterations for the generalized Lipschitzian and -strongly pseudocontractive mappings in real uniformly smooth Banach spaces. Our results significantly generalize the recent known results of [B. E. Rhoades and S. M. Soltuz, The equivalence of Mann iteration and Ishikawa iteration for non-Lipschitz operators, Int. J. Math. Math. Sci. 42 (2003), 2645.2651].

In this paper, we show the equivalence of convergence between the modified Mann and Ishikawa iterations with errors for an asymptotically pseudocontractive mapping under the condition of removing the bounded assumption. We also point out the problems of (Rhoades and Soltuz in J. Math. Anal. Appl. 283:681-688, 2003; Xue in Bull. Korean Math. Soc. 47(2):295-305, 2010; Xue in J. Math. Inequal. 4(3):345-354, 2010), extend and improve the results of (Zeng in Acta Math. Sin. 47(2):219-228, 2004).

In this paper, we establish some strong convergence theorems of the modified Ishikawa and Mann iterations with errors of uniformly L-Lipschitzian asymptotically pseudocontractive mappings in real Banach spaces. Our results not only provide the new proof method, but also extend the known corresponding results given in (Chang in Proc. Am. Math. Soc. 129:845-853, 2001; Chang et al. in Appl. Math. Lett. 22:121-125, 2009; Goebel and Kirk in Proc. Am. Math. Soc. 35:171-174, 1972; Ofoedu in J. Math. Anal. Appl. 321:722-728, 2006; Schu in J. Math. Anal. Appl. 158:407-413, 1991). In order to get some applications of our results, we also provide specific examples.

Our aim in this paper is to illustrate that the proof of main theorem of Rhoades and Şoltuz (2003) concerning the equivalence between the convergences of Ishikawa and Mann iterations for uniformlyL-Lipschitzian asymptotically pseudocontractive maps is incorrect and to provide its correct version.

The evolution of institutional arrangements in Chinese agriculture is looked at through the twin concepts of necessity and purpose. Nested agency relations are examined from the state planning appa...

It is shown that the convergence of the multistep iterative process with errors is obtained for uniformly continuousΦ-hemicontractive mappings in real Banach spaces. We also revise the problems of C. E. Chidume and C. O. Chidume (2005).

LetEbe an arbitrary uniformly smooth real Banach space, letDbe a nonempty closed convex subset ofE, and letT:D→Dbe a uniformly generalized Lipschitz generalized asymptoticallyΦ-strongly pseudocontractive mapping withq∈F(T)≠∅. Let{an},{bn},{cn},{dn}be four real sequences in[0,1]and satisfy the conditions: (i)an+cn≤1,bn+dn≤1; (ii)an,bn,dn→0asn→∞andcn=o(an); (iii)Σn=0∞an=∞. For somex0,z0∈D, let{un},{vn},{wn}be any bounded sequences inD, and let{xn},{zn}be the modified Ishikawa and Mann iterative sequences with errors, respectively. Then the convergence of{xn}is equivalent to that of{zn}.

According to the equivalent circuit of the DC motor, the dynamical model of the motor is investigated firstly. Then, the dynamical model for the hybrid-driven press is developed using Lagrangepsilas formulation. The systempsilas equation is derived using expressions for the system energy function, its partial and time derivatives with respect to the defined generalized coordinates. The dynamical equation is then transformed into a system of first order equations. Based on the control theory, the PID control model of the hybrid-driven press is set up. Then the proportional gain, differential gain and integral gain are optimized. The fourth order Runge-Kutta method is chosen as the integration technique of computer simulation and the time history of the hybrid-driven press is obtained.

We show the equivalence of the convergence of Picard and Krasnoselskij, Mann, and Ishikawa iterations for the quasi-contraction mappings in convex metric spaces.

In this note, we point out several gaps in Gurudwan and Sharma (Appl. Math. Comput. 217(15):6748-6754, 2011) and Yang (Appl. Math. Comput. 218(21):10367-10369, 2012) and give the main results under weaker conditions. MSC: 47H10; 47H09; 46B20

We provide sufficient conditions for Picard iteration to converge faster than Krasnoselskij, Mann, Ishikawa, or Noor iteration for quasicontractive operators. We also compare the rates of convergence between Krasnoselskij and Mann iterations for Zamfirescu operators.

In this paper, under the new condition we show that the convergence of the modified Mann and Ishikawa iterations is equivalent for uniformly L-Lipschitz asymptotically pseudocontractive mappings in real Banach spaces. Our results extend and improve the corresponding results of Zeng (Acta Math. Sin. 47:219-228, 2004).

Let D be a nonempty closed convex subset of an arbitrary uniformly smooth real Banach space E, and be a generalized Lipschitz Φ-hemi-contractive mapping with . Let , , , be four real sequences in and satisfy the conditions (i) as and ; (ii) . For some , let , be any bounded sequences in D, and be an Ishikawa iterative sequence with errors defined by (1.1). Then (1.1) converges strongly to the fixed point q of T. A related result deals with the operator equations for a generalized Lipschitz and Φ-quasi-accretive mapping. MSC:47H10.

Let E be a real Banach space and let D be a nonempty closed convex subset of E ,l et T : D → D be a continuous weak generalized ϕ-hemicontractive mapping. The existence theorem of a fixed point of a weak generalized ϕ-pseudocontractive mapping is obtained. And we also prove that implicit Mann and Ishikawa iterations converge strongly to the unique fixed point of T. Our results extend the corresponding results of Xiang (Nonlinear Anal. 70(6): 2277-2279, 2009). MSC: Primary 47H09; 47J25

The purpose of this paper is to characterize conditions for the convergence of the implicit Ishikawa iterative scheme with errors in the sense of Agarwal et al. (J. Math. Anal. Appl. 272:435-447, 2002) to a common fixed point of two ϕ-hemicontractive mappings in a nonempty convex subset of an arbitrary Banach space.