• Title/Summary/Keyword: coincidence theorem

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COINCIDENCE THEOREMS FOR NONCOMPACT ℜℭ-MAPS IN ABSTRACT CONVEX SPACES WITH APPLICATIONS

  • Yang, Ming-Ge;Huang, Nan-Jing
    • Bulletin of the Korean Mathematical Society
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    • v.49 no.6
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    • pp.1147-1161
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    • 2012
  • In this paper, a coincidence theorem for a compact ${\Re}\mathfrak{C}$-map is proved in an abstract convex space. Several more general coincidence theorems for noncompact ${\Re}\mathfrak{C}$-maps are derived in abstract convex spaces. Some examples are given to illustrate our coincidence theorems. As applications, an alternative theorem concerning the existence of maximal elements, an alternative theorem concerning equilibrium problems and a minimax inequality for three functions are proved in abstract convex spaces.

EXISTENCE OF COINCIDENCE POINT UNDER GENERALIZED NONLINEAR CONTRACTION WITH APPLICATIONS

  • Deshpande, Bhavana;Handa, Amrish;Thoker, Shamim Ahmad
    • East Asian mathematical journal
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    • v.32 no.3
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    • pp.333-354
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    • 2016
  • We present coincidence point theorem for g-non-decreasing mappings satisfying generalized nonlinear contraction on partially ordered metric spaces. We show how multidimensional results can be seen as simple consequences of our unidimensional coincidence point theorem. We also obtain the coupled coincidence point theorem for generalized compatible pair of mappings $F,G:X^2{\rightarrow}X$ by using obtained coincidence point results. Furthermore, an example and an application to integral equation are also given to show the usability of obtained results. Our results generalize, modify, improve and sharpen several well-known results.

MULTIDIMENSIONAL COINCIDENCE POINT RESULTS FOR CONTRACTION MAPPING PRINCIPLE

  • Handa, Amrish
    • The Pure and Applied Mathematics
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    • v.26 no.4
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    • pp.277-288
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    • 2019
  • The main objective of this article is to establish some coincidence point theorem for g-non-decreasing mappings under contraction mapping principle on a partially ordered metric space. Furthermore, we constitute multidimensional results as a simple consequences of our unidimensional coincidence point theorem. Our results improve and generalize various known results.

TRIPLED COINCIDENCE AND COMMON TRIPLED FIXED POINT THEOREM FOR HYBRID PAIR OF MAPPINGS SATISFYING NEW CONTRACTIVE CONDITION

  • Deshpande, Bhavana;Handa, Amrish
    • East Asian mathematical journal
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    • v.32 no.5
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    • pp.701-716
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    • 2016
  • We establish a tripled coincidence and common tripled fixed point theorem for hybrid pair of mappings satisfying new contractive condition. To find tripled coincidence points, we do not use the continuity of any mapping involved therein. An example is also given to validate our result. We improve, extend and generalize several known results.

NOTES ON RANDOM FIXED POINT THEOREMS

  • Cho Y.J.;Khan M. Firdosh;Salahuddin Salahuddin
    • The Pure and Applied Mathematics
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    • v.13 no.3 s.33
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    • pp.227-236
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    • 2006
  • The purpose of this paper is to establish a random fixed point theorem for nonconvex valued random multivalued operators, which generalize known results in the literature. We also derive a random coincidence fixed point theorem in the noncompart setting.

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COINCIDENCE POINT AND FIXED POINT THEOREMS IN PARTIAL METRIC SPACES FOR CONTRACTIVE TYPE MAPPINGS WITH APPLICATIONS

  • SALUJA, G.S.;KIM, JONG KYU;LIM, WON HEE
    • Journal of applied mathematics & informatics
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    • v.40 no.5_6
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    • pp.1053-1071
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    • 2022
  • The purpose of this article is to establish some fixed point theorems, a common fixed point theorem and a coincidence point theorem via contractive type condition in the framework of complete partial metric spaces and give some examples in support of our results. As an application to the results, we give some fixed point theorems for integral type contractive conditions. The results presented in this paper extend and generalize several results from the existing literature.

SELECTION THEOREMS WITH n-CONNECTDENESS

  • In-Sook Kim
    • Journal of the Korean Mathematical Society
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    • v.35 no.1
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    • pp.165-175
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    • 1998
  • We give a generalization of the selection theorem of Ben-El-Mechaiekh and Oudadess to complete LD-metric spaces with the aid of the notion of n-connectedness. Our new selection theorem is used to obtain new results of fixed points and coincidence points for compact lower semicontinuous set-valued maps with closed values consisting of D-sets in a complete LD-metric space.

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HUGE CONTRACTION ON PARTIALLY ORDERED METRIC SPACES

  • DESHPANDE, BHAVANA;HANDA, AMRISH;KOTHARI, CHETNA
    • The Pure and Applied Mathematics
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    • v.23 no.1
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    • pp.35-51
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    • 2016
  • We establish coincidence point theorem for g-nondecreasing mappings satisfying generalized nonlinear contraction on partially ordered metric spaces. We also obtain the coupled coincidence point theorem for generalized compatible pair of mappings F, G : X2 → X by using obtained coincidence point results. Furthermore, an example is also given to demonstrate the degree of validity of our hypothesis. Our results generalize, modify, improve and sharpen several well-known results.

THE EXISTENCE OF PERIODIC SOLUTION OF A TWO-PATCHES PREDATOR-PREY DISPERSION DELAY MODELS WITH FUNCTIONAL RESPONSE

  • Zhang, Zhengqiu;Wang, Zhicheng
    • Journal of the Korean Mathematical Society
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    • v.40 no.5
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    • pp.869-881
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    • 2003
  • In this paper, a nonautonomous predator-prey dispersion delay models with functional response is studied. By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for above models is established.