• Title/Summary/Keyword: unique common fixed point

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EXISTENCE AND UNIQUENESS OF FIXED POINT OF SOME EXPANSIVE-TYPE MAPPINGS IN GENERALIZED MODULAR METRIC SPACES

  • Godwin Amechi Okeke;Daniel Francis;Jong Kyu Kim
    • Nonlinear Functional Analysis and Applications
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    • v.28 no.4
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    • pp.957-988
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    • 2023
  • We define new classes of expansive-type mappings in the setting of modular 𝜔G-metric spaces and prove the existence of common unique fixed point for these classes of expansive-type mappings on 𝜔G-complete modular 𝜔G-metric spaces. The results established in this paper extend, improve, generalize and compliment many existing results in literature. We produce some examples to validate our results.

AN EXPERIMENTAL STUDY ON THE TISSUE RESPONSE OF THE TEMPOROMANDIBULAR JOINT IN UNILATERAL MANDIBULAR EDENTULISM (하악편측치아의 결손에 따른 악관절의 조직반응에 대한 연구)

  • Paik, Hyee-Seon;Kim, Yung-Soo
    • The Journal of Korean Academy of Prosthodontics
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    • v.29 no.2
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    • pp.285-294
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    • 1991
  • The human temporomandibular joint as a ginglymoarthrodial one has much in common with the other synovial joints of the body, but it does possess an unique charachteristic in that it must accomodate the various occlusal relations of dentition during an end point of closure. For that reason, the movement of the condyle in the temporomandibular joint is susceptible to influences from the nature of occlusion. Undue loading to the temporomandibular joint can be applied on the occasion of premature contacts in centric relation, balancing side interferences, change of occlusal surfaces due to excessive attrition, loss of tooth. Such occlusal disharmonies in association with the systemic and emotional factors may give rise to the temporomandibular disorder. On the other hand, the changes of occlusal patterns in the growing body can also have an effect on the growth of the temporomandibular joint through the alterations of functional stresses. The purpose of this study was to observe histopathologic response of the temporomandibular joint in unilateral chewing on one side exclusively for 10 months. Three dogs showing normal masticatory function were chosen. One dog aged about 12 months was for control, two dogs for experimental specimens were about 12 and 18 months old respectively. For chewing on the left side only, unilateral lower right premolar and molar were extracted in two experimental specimens. And then three dogs were sacrificed 10 months later. Frontal histologic sectioning of joints were done for the observation of the effects of one-side chewing. 24 specimens from three dogs were obtained and fixed in 10% formalin and routinly processed with H-E staining for histologic examination. The light microscopic findings were interpretated as follows: 1. Experimental specimen 1 aged about 22 months: In comparison with control and right non-chewing side, the proliferative and hypertrophic zone were increased at the mesial and lateral part of left chewing side condyle. There was no change of the articular tissue of temporal bone. 2. Experimental specimen 2 aged about 28 months: The articular tissues of adult joint were observed. The differences between the chewing and non-chewing side were not seen in the articular tissues of condyle and temporal bone.

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