Some fixed point theorems for generalized Kannan type mappings in b-metric spaces

Haokip, Nehjamang; Goswami, Nilakshi

doi:10.22199/issn.0717-6279-2019-04-0050

Cited by 12 publications

(10 citation statements)

References 17 publications

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“…Garai et al [29] and Haokip and Goswami [33] defined Φ -orbitally compact metric spaces and Φ-orbitally compact b-metric spaces, respectively, which extend sequentially compact metric (b-metric) spaces. Now, the similar definition of Φ-orbital compactness and a fixed point theorem of Ćirić-type b-quasicontraction in cone b-metric spaces over Banach algebras is showed.…”

Section: Orbital Compactnessmentioning

confidence: 99%

Fixed Points and Continuity Conditions of Generalized $b$ -Quasicontractions

Han

2022

Journal of Function Spaces

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In this research, we first check that the abstract cone b -metric is discontinuous in the case of normal cone by a counter example. We obtain several meaningful results about generalized b -quasicontraction and Ćirić-type b -quasicontraction in cone b -metric spaces over Banach algebras, weakening certain important conditions of the spaces and the mappings. Meanwhile, several valid examples are given to demonstrate the new notions and fixed point results, when the existing theorems in the literature are not applicable.

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Section: Orbital Compactnessmentioning

confidence: 99%

Fixed Points and Continuity Conditions of Generalized $b$ -Quasicontractions

Han

2022

Journal of Function Spaces

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“…e concepts of bounded compactness and T-orbital compactness were discussed in usual metric spaces [7] and b-metric spaces [8], which were important to weaken the condition of compactness. In the following, we give the notions of generalized Kannan-type and Reich-Ćirić-Rustype contractions, bounded compactness, and T-orbital compactness in the framework of cone b-metric spaces over Banach algebras, which are generalizations of metric spaces and b-metric spaces.…”

Section: Bounded Compactness and T-orbital Compactnessmentioning

confidence: 99%

“…In order to improve these theorems, Garai et al [7] investigated some meaningful fixed point theorems of Kannan-type contractive mappings in metric spaces by using the notions of bounded compactness, orbital continuity, and T-orbital compactness. Afterwards, Haokip and Goswami [8] extended some related results in b-metric spaces by using a subadditive altering distance function. In this paper, we further study the fixed point theorems about Kannan-type and Reich-Ćirić-Rus-type contractions in a much broader space.…”

Section: Introductionmentioning

confidence: 99%

Generalized Reich–Ćirić–Rus-Type and Kannan-Type Contractions in Cone $b$ -Metric Spaces over Banach Algebras

Han

2021

Journal of Mathematics

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In this paper, we firstly introduce the generalized Reich‐Ćirić‐Rus-type and Kannan-type contractions in cone b -metric spaces over Banach algebras and then obtain some fixed point theorems satisfying these generalized contractive conditions, without appealing to the compactness of X . Secondly, we prove the existence and uniqueness results for fixed points of asymptotically regular mappings with generalized Lipschitz constants. The continuity of the mappings is deleted or relaxed. At last, we prove that the completeness of cone b -metric spaces over Banach algebras is necessary if the generalized Kannan-type contraction has a fixed point in X . Our results greatly extend several important results in the literature. Moreover, we present some nontrivial examples to support the new concepts and our fixed point theorems.

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“…In 1988, Grabiec [7] introduced fixed point theory in fuzzy metric spacesby extending different existing results to such spaces. During the recent decades, the study of different generalized classes of nonexpansive mappings and the related fixed point theorems in different spaces have found much importance due to many practical applications (refer to [2,3,4,5,7,9,10,11,12,13,17,18,20,25,26]). Several research workers have interesting contribution (refer to [6,8,14,15,19,24]) in this regard.…”

Section: Introductionmentioning

confidence: 99%