• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.459-465
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• 2002

In this paper, axed point theorems for contractive and expansive maps are established, some of which extend a few results of Das and Debata, Edelstein, Fisher, Leader, Shih and Yeh, and Jungck.

• Journal of the Korean Mathematical Society
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• v.38 no.3
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• pp.669-681
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• 2001

This paper introduces the notions of essential and inessential map for countably $textsc{k}$-set contractive maps. These ideas enable us to establish a Krasnoselskii-Petryshyn compression and expansion theorem in a cone for countably $textsc{k}$-set contractive maps.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.397-409
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• 2010

We prove the existence of common fixed points for multivalued maps satisfying a contractive condition of an integral type. Our results are extent ions of results of Feng and Liu[Y. Feng, S. Liu, Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings, J. Math. Anal. Appl. 317(2006), 103-112] and also, extent ions of results of Daffer and Kaneko[P. Z. Daffer, H. Kaneko, Fixed points of generalized contractive multi-valued map pings, J. Math. Anal. Appl. 192(1995), 655-666]. A main result in Feng and Liu[Y. Feng, S. Liu, Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings, J. Math. Anal. Appl. 317(2006), 103-112] is proved under necessary additional conditions.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.1027-1035
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• 2011

In this paper, we introduce the concept of generalized weak q-contractivity for multivalued maps defined on quasi-metric spaces. A new fixed point theorem for these maps is established. The convergene of iterate schem of the form $x_n+1\;{\in}\;Fx_n$ is investigated. And a new periodic point theorem for weakly q-contractive self maps of quasi-metric spaces is proved.

• Bulletin of the Korean Mathematical Society
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• v.30 no.2
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• pp.201-212
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• 1993

It is our purpose in this paper to first establish an inequality in real uniformly smooth Banach spaces with modulus of smoothness of power type q > 1 that generalizes a well known Hilbert space inequality. Using our inequality, we shall then extend the above result of Qihou [15] on the Ishikawa iteration process from Hilbert spaces to these much more general Banach spaces. Furthermore, we shall prove that the Mann iteration process converges strongly to the unique fixed point of a quasi-contractive map in this general setting. No compactness assumption on K is required in our theorems.

• Journal of the Chungcheong Mathematical Society
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• v.18 no.1
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• pp.51-64
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• 2005

The object of this paper is to prove two unique common fixed point theorems for a pair of a set-valued map and a self map satisfying a general contractive condition using orbital concept and weak-compatibility of the pair. One of these results generalizes substantially, the result of Dhage, Jennifer and Kang [4]. Simultaneously, its implications for two maps and one map improves and generalizes the results of Dhage [3], and Rhoades [11]. All the results of this paper are new.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.327-343
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• 2006

A general methodology is suggested to solve shelf-space allocation problem of retailers. A multi-item inventory model of breakable items is developed, where items are either complementary or substitute. Demands of the items depend on the amount of stock on the showroom and unit price of the respective items. Also demand of one item decreases (increases) due to the presence of others in case of substitute (complementary) product. For such a model, a Contractive Mapping Genetic Algorithm (CMGA) has been developed and implemented to find the values of different decision variables. These are evaluated to have maximum possible profit out of the proposed system. The system has been illustrated numerically and results for some particular cases are derived. The results are compared with some other heuristic approaches- Simulated Annealing (SA), simple Genetic Algorithm (GA) and Greedy Search Approach (GSA) developed for the present model.

• Kyungpook Mathematical Journal
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• v.63 no.1
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• pp.45-60
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• 2023

In this paper we suggest an enhanced Geraghty-type contractive mapping for examining the existence properties of classical nonlinear operators with or without prior degenerates. The nonlinear operators are proved to exist with the imposition of the Geraghty-type condition in a non-empty closed subset of complete metric spaces. To showcase some efficacies of the Geraghty-type condition, convergent rate and stability are deduced. The results are used to study some asymptotic properties of perturbed integral and hypergeometric operators. The results also extend and generalize some existing Geraghty-type conditions.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.571-577
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• 1997

We first show that if $\psi : M_n(B(H)) \to M_n (B(H))$ is a $D_n \otimes F(H)$-bimodule map, then there is a matrix $A \in M_n$ such that $\psi = S_A$. Secondly, we show that for an operator space $\varepsilon, A \in M_n$, the Schur product map $S_A : M_n(\varepsilon) \to M_n(\varepsilon)$ and $\phi_A : M_n(\varepsilon) \to \varepsilon$, defined by $\phi_A([x_{ij}]) = \sum^{n}_{i,j=1}{a_{ij}x_{ij}}$, we have $\Vert S_A \Vert = \Vert S_A \Vert_{cb} = \Vert A \Vert_S, \Vert \phi_A \Vert = \Vert \phi_A \Vert_{cb} = \Vert A \Vert_1$ and obtain some characterizations of A for which $S_A$ is contractive.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.743-752
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• 2011

Fixed point theorems for two hybrid pairs of single valued and multivalued noncompatible maps under strict contractive condition are proved, without appeal to continuity of any map involved therein and completeness of underlying space. These results extend, unify and improve the earlier comparable known results.