• Title/Summary/Keyword: Multivalued map

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COMMON FIXED POINT THEOREMS FOR MULTIVALUED MAPS SATISFYING CONTACTIVE CONDITIONS OF AN INTEGRAL TYPE

  • Cho, Seong-Hoon;Bae, Jong-Sook
    • 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.

FIXED AND PERIODIC POINT THEOREMS IN QUASI-METRIC SPACES

  • Cho, Seong-Hoon;Lee, Jee-Won
    • 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.

Second Order Impulsive Neutral Functional Differential Inclusions

  • Liu, Yicheng;Li, Zhixiang
    • Kyungpook Mathematical Journal
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    • v.48 no.1
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    • pp.1-14
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    • 2008
  • In this paper, we investigate the existence of solutions of second order impulsive neutral functional differential inclusions which the nonlinearity F admits convex and non-convex values. Some results under weaker conditions are presented. Our results extend previous ones. The methods rely on a fixed point theorem for condensing multivalued maps and Schaefer's fixed point theorem combined with lower semi-continuous multivalued operators with decomposable values.

COMMON FIXED POINTS OF A WEAK-COMPATIBLE PAIR OF A SINGLE VALUED AND A MULTIVALUED MAPS IN D-METRIC SPACES

  • Singh, Bijendra;Jain, Shobha
    • 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.

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COMMON FIXED POINTS OF A LIMIT WEAK COMPATIBLE PAIR OF A MULTIVALUED MAPPING AND A SINGLE VALUED MAPPING IN D-METRIC SPACES

  • Singh, Bijendra;Jain, Shobha;jain, Shishir
    • East Asian mathematical journal
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    • v.22 no.1
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    • pp.35-51
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    • 2006
  • This paper deals with a general contraction. Two fixed-point theorems for a limit weak-compatible pair of a multi-valued map and a self map on a D-metric space have been established. These results improve significantly, the main results of Dhage, Jennifer and Kang [5] by reducing its assumption and generalizing its contraction simultaneously. At the same time some results of Singh, Jain and Jain [12] are generalized from a self map to a pair of a set-valued and a self map. Theorems of Veerapandi and Rao [16] get generalized and improved by these results. All the results of this paper are new.

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RANDOM FIXED POINT THEOREMS FOR *-NONEXPANSIVE OPERATORS IN FRECHET SPACES

  • Abdul, Rahim-Khan;Nawab, Hussain
    • Journal of the Korean Mathematical Society
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    • v.39 no.1
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    • pp.51-60
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    • 2002
  • Some random fixed point theorems for nonexpansive and *-nonexpansive random operators defined on convex and star-shaped sets in a Frechet space are proved. Our work extends recent results of Beg and Shahzad and Tan and Yaun to noncontinuous multivalued random operators, sets analogue to an earlier result of Itoh and provides a random version of a deterministic fixed point theorem due to Singh and Chen.

COINCIDENCE AND COMMON FIXED POINTS OF NONCOMPATIBLEMAPS

  • Beg, Ismat;Abbas, Mujahid
    • 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.