• Kyungpook Mathematical Journal
• /
• v.63 no.3
• /
• pp.451-461
• /
• 2023

In this paper, we study the fixed point property for generalized asymptotically nonexpansive mappings in the setting of p-Hadamard spaces, with p ≥ 2. We prove the strong convergence of the sequence generated by the modified two-step iterative sequence for finding a fixed point of a generalized asymptotically nonexpansive mapping in p-Hadamard spaces.

• Journal of the Korean Mathematical Society
• /
• v.59 no.3
• /
• pp.549-570
• /
• 2022

In this paper, we study the Birkhoff's ergodic theorem on geodesic metric spaces, especially on Hadamard spaces, using the notion of weighted inductive means. Also, we study a deterministic weighted sequence for the weighted Birkhoff's ergodic theorem in Hadamard spaces.

• Communications of the Korean Mathematical Society
• /
• v.31 no.3
• /
• pp.483-493
• /
• 2016

In this paper, we study and prove common fixed point theorems for N generalized I-asymptotically nonexpansive mappings in a Hadamard space.

• Journal of applied mathematics & informatics
• /
• v.29 no.3_4
• /
• pp.859-868
• /
• 2011

In this article, by considering error inequalities, we propose a new way to treat the Fej$\'{e}$r and Hermite-Hadamard inequalities involving n knots and m-th derivative on H$\"{o}$lder spaces. Moreover, some new related estimations are also given.

• Honam Mathematical Journal
• /
• v.30 no.2
• /
• pp.335-341
• /
• 2008

In this paper, we use the convexity of distance function between geodesics in a singular Hadamard space to generalize Hadamard-Cartan theorem for 2-dimensional metric spaces. We also determine a neighborhood of a closed geodesic where no other closed geodesic exists in a complete space of nonpositive curvature.

• Nonlinear Functional Analysis and Applications
• /
• v.27 no.1
• /
• pp.45-58
• /
• 2022

In this paper, iterative algorithms for approximating a common fixed point of a countable family of multi-valued demicontractive maps in the setting of Hadamard spaces are presented. Under different mild conditions, the sequences generated are shown to strongly convergent and ∆-convergent to a common fixed point of the considered family, accordingly. Our theorems complement many results in the literature.

• Journal of the Korean Mathematical Society
• /
• v.38 no.6
• /
• pp.1191-1204
• /
• 2001

The paper is devoted to the study of fractional integration and differentiation on a finite interval [a, b] of the real axis in the frame of Hadamard setting. The constructions under consideration generalize the modified integration $\int_{a}^{x}(t/x)^{\mu}f(t)dt/t$ and the modified differentiation ${\delta}+{\mu}({\delta}=xD,D=d/dx)$ with real $\mu$, being taken n times. Conditions are given for such a Hadamard-type fractional integration operator to be bounded in the space $X^{p}_{c}$(a, b) of Lebesgue measurable functions f on $R_{+}=(0,{\infty})$ such that for c${\in}R=(-{\infty}{\infty})$, in particular in the space $L^{p}(0,{\infty})\;(1{\le}{\le}{\infty})$. The existence almost every where is established for the coorresponding Hadamard-type fractional derivative for a function g(x) such that $x^{p}$g(x) have $\delta$ derivatives up to order n-1 on [a, b] and ${\delta}^{n-1}[x^{\mu}$g(x)] is absolutely continuous on [a, b]. Semigroup and reciprocal properties for the above operators are proved.

• Kyungpook Mathematical Journal
• /
• v.29 no.1
• /
• pp.7-10
• /
• 1989

• Communications of the Korean Mathematical Society
• /
• v.39 no.2
• /
• pp.421-436
• /
• 2024

In this article, we propose a shrinking projection algorithm for solving a finite family of generalized equilibrium problem which is also a fixed point of a nonexpansive mapping in the setting of Hadamard manifolds. Under some mild conditions, we prove that the sequence generated by the proposed algorithm converges to a common solution of a finite family of generalized equilibrium problem and fixed point problem of a nonexpansive mapping. Lastly, we present some numerical examples to illustrate the performance of our iterative method. Our results extends and improve many related results on generalized equilibrium problem from linear spaces to Hadamard manifolds. The result discuss in this article extends and complements many related results in the literature.

• Korean Journal of Mathematics
• /
• v.30 no.3
• /
• pp.467-474
• /
• 2022

In this article, we consider the integral operator 𝓒^b,c, which is defined as follows: $${\mathcal{C}}^{b,c}(f)(z)={\displaystyle\smashmargin{2}{\int\nolimits_{0}}^z}{\frac{f(w)*F(1,1;c;w)}{w(1-w)^{b+1-c}}}dw,$$ where * denotes the Hadamard/ convolution product of power series, F(a, b; c; z) is the classical hypergeometric function with b, c > 0, b + 1 > c and f(0) = 0. We investigate the boundedness of the 𝓒^b,c operators on Bloch spaces.