• 대한수학회논문집
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• 제31권4호
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• pp.845-855
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• 2016

We introduce the proximal point algorithm in a p-uniformly convex metric space. We first introduce the notion of p-resolvent map in a p-uniformly convex metric space as a generalization of the Moreau-Yosida resolvent in a CAT(0)-space, and then we secondly prove the convergence of the proximal point algorithm by the p-resolvent map in a p-uniformly convex metric space.

• 대한수학회보
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• 제42권3호
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• pp.623-629
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• 2005

Inclusion relations under certain integral operators are proved for k-uniformly starlike functions. These results are also extended to k-uniformly convex, close-to-convex, and quasi-convex functions

• Kyungpook Mathematical Journal
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• 제58권2호
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• pp.243-255
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• 2018

We introduce several k-uniformly subclasses of p-valent functions defined by the generalized fractional differintegral operator and investigate various inclusion relationships for these subclasses. Some interesting applications involving certain classes of integral operators are also considered.

• Kyungpook Mathematical Journal
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• 제55권2호
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• pp.383-394
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• 2015

In this paper, we define two new subclass of k-uniformly starlike and convex functions of order ${\alpha}$ type ${\beta}$ with varying argument of coefficients. Further, we obtain coefficient estimates, extreme points, growth and distortion bounds, radii of starlikeness, convexity and results on modified Hadamard products.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.715-723
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• 2009

The aim of this paper is to present an explicit iteration method for finding a common fixed point of a finite family of strictly pseudocon-tractive mappings defined on q-uniformly smooth and uniformly convex Banach spaces.

• 호남수학학술지
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• 제16권1호
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• pp.41-45
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• 1994

• Journal of applied mathematics & informatics
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• 제3권1호
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• pp.47-54
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• 1996

We prove that if RUC(S) has a left invariant mean ${\rho}={T_{S} : s \;{\in}\; S}$ is a continuous repesentation of S as nonexpansive map-pings on a closed convex subset C of a p-uniformly convex and p-uniformly smooth Banach space and C contains an element of bounded orbit then C contains a common fixed point for ${\rho}$.

• Journal of applied mathematics & informatics
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• 제39권5_6호
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• pp.717-723
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• 2021

The purpose of the present paper is to give sufficient conditions for normalized Dini function which is the special combination of the generalized Bessel function of first kind to be in the classes k-starlike functions and k-uniformly convex functions.

• East Asian mathematical journal
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• 제24권1호
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• pp.81-95
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• 2008

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, and $T\;:\;C\;{\rightarrow}\;E$ a nonexpansive mapping satisfying the weak inwardness condition. Assume that every weakly compact convex subset of E has the fixed point property. For $f\;:\;C\;{\rightarrow}\;C$ a contraction and $t\;{\in}\;(0,\;1)$, let $x_t$ be a unique fixed point of a contraction $T_t\;:\;C\;{\rightarrow}\;E$, defined by $T_tx\;=\;tf(x)\;+\;(1\;-\;t)Tx$, $x\;{\in}\;C$. It is proved that if {$x_t$} is bounded, then $x_t$ converges to a fixed point of T, which is the unique solution of certain variational inequality. Moreover, the strong convergence of other implicit and explicit iterative schemes involving the sunny nonexpansive retraction is also given in a reflexive and strictly convex Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm.

• Korean Journal of Mathematics
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• 제21권3호
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• pp.325-330
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• 2013

In this paper, we prove Trotter-Kato theorem in the weak topology if $X^*$ is a uniformly convex Banach space.