• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.665-669
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• 2002

In this paper, we study averaging properties in Banach space. We prove that the convex block Banach-Saks property is equivalent to the reflexivity in a Banach space. And we show that a weakly compact operator is a convex block Banach-Saks operator.

• East Asian mathematical journal
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• v.27 no.1
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• pp.35-49
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• 2011

In this paper, we study multi-step iterative algorithm with errors and give the necessary and sufficient condition to converge to com mon fixed points for a finite family of asymptotically quasi-nonexpansive type mappings in Banach spaces. Also we have proved a strong convergence theorem to converge to common fixed points for a finite family said mappings on a nonempty compact convex subset of a uniformly convex Banach spaces. Our results extend and improve the corresponding results of [2, 4, 7, 8, 9, 10, 12, 15, 20].

• Korean Journal of Mathematics
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• v.19 no.1
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• pp.1-16
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• 2011

In this paper, using differential operator, we have introduce new class of p-valent uniformly convex functions in the unit disc U = {z : |z| < 1} and obtain the coefficient bounds, extreme bounds and radius of starlikeness for the functions belonging to this generalized class. Furthermore, partial sums $f_k(z)$ of functions $f(z)$ in the class $S^*({\lambda},{\alpha},{\beta})$ are considered. The various results obtained in this paper are sharp.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.275-285
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• 1997

Let E be a uniformly convex Banach space with a uniformly G$\hat{a}teaux differentiable norm, C a nonempty closed convex subset of $E, T : C \to E$ a nonexpansive mapping, and Q a sunny nonexpansive retraction of E onto C. For $u \in C$ and $t \in (0,1)$, let $x_t$ be a unique fixed point of a contraction $R_t : C \to C$, defined by $R_tx = Q(tTx + (1-t)u), x \in C$. It is proved that if ${x_t}$ is bounded, then the strong $lim_{t\to1}x_t$ exists and belongs to the fixed point set of T. Furthermore, the strong convergence of ${x_t}$ in a reflexive and strictly convex Banach space with a uniformly G$\hat{a}$teaux differentiable norm is also given in case that the fixed point set of T is nonempty.

• Korean Journal of Mathematics
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• v.30 no.4
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• pp.665-678
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• 2022

The aim of this paper is to introduce a new iterative process and show that our iteration scheme is faster than other existing iteration schemes with the help of numerical examples. Next, we have established convergence and stability results for the approximation of fixed points of the contractive-like mapping in the framework of uniformly convex Banach space. In addition, we have established some convergence results for the approximation of the fixed points of a nonexpansive mapping.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.1-14
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• 2024

In this paper, we establish strong and ∆-convergence theorems for new iteration process namely S-R iteration process for a generalized α-nonexpansive mappings in a uniformly convex hyperbolic space and also we show that our iteration process is faster than other iteration processes appear in the current literature's. Our results extend the corresponding results of Ullah et al. [5], Imdad et al. [16] in the setting of uniformly convex hyperbolic spaces and many more in this direction.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.325-336
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• 2008

In this paper, we prove the weak and strong convergence of the three-step iterative scheme with errors to a common fixed point for two asymptotically nonexpansive mappings in a uniformly convex Banach space under a condition weaker than compactness. Our theorems improve and generalize some previous results.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.83-95
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• 2014

In a uniformly convex Banach space, we introduce a iterative scheme for a finite family of asymptotically quasi-nonexpansive mappings and utilize a new inequality to prove several convergence results for the iterative sequence. The results generalize and unify many important known results of relevant scholars.

• East Asian mathematical journal
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• v.26 no.1
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• pp.81-93
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• 2010

In this paper, a strong convergence theorem of multi-step iterative schemes with errors for asymptotically quasi-nonexpansive type nonself mappings is established in a real uniformly convex Banach space. Our results extend the corresponding results of Wangkeeree [12], Xu and Noor [13], Kim et al.[1,6,7] and many others.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.525-536
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• 2007

In this paper, we prove the weak and strong convergence of the Noor iterative scheme to a common fixed point for two asymptotically nonexpansive mappings in a uniformly convex Banach space under a condition weaker than compactness. Our theorems improve and generalize some previous results.