Study of multivalued fixed point problems for generalized contractions in double controlled dislocated quasi metric type spaces

Tahair Rasham; Abdullah Shoaib; Shaif Alshoraify; Choonkil Park; Jung Rye Lee; Tahair Rasham; Abdullah Shoaib; Shaif Alshoraify; Choonkil Park; Jung Rye Lee

doi:10.3934/math.2022063

AIMS Mathematics

2022, Volume 7, Issue 1: 1058-1073. doi: 10.3934/math.2022063

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Research article

Study of multivalued fixed point problems for generalized contractions in double controlled dislocated quasi metric type spaces

1.
Department of Mathematics, University of Poonch Rawalakot, Azad Kashmir, Pakistan
2.
Department of Mathematics and Statistics, Riphah International University, Islamabad, Pakistan
3.
Department of Mathematics and Statistics, International Islamic University, H-10, Islamabad-44000, Pakistan
4.
Department of Mathematics, Research Institute for Natural Science, Hanyang University, Seoul 04763, Korea
5.
Department of Data Sciences, Daejin University, Kyunggi 11159, Korea

Received: 13 June 2021 Accepted: 16 September 2021 Published: 19 October 2021
MSC : 46S40, 54H25, 47H10

The main purpose of this research is to establish a new generalized $ \xi^{\ast } $-Kannan type double controlled contraction on a sequence and obtain fixed point results for a pair of multivalued mappings in left $ K $-sequentially complete double controlled dislocated quasi metric type spaces. New results in different setting of generalized metric spaces and ordered spaces and also new results for graphic contractions can be obtained as corollaries of our results. An example is presented to show the novelty of results. In this paper, we unify and extend some recent results in the existing literature.
Citation: Tahair Rasham, Abdullah Shoaib, Shaif Alshoraify, Choonkil Park, Jung Rye Lee. Study of multivalued fixed point problems for generalized contractions in double controlled dislocated quasi metric type spaces[J]. AIMS Mathematics, 2022, 7(1): 1058-1073. doi: 10.3934/math.2022063

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Abstract

The main purpose of this research is to establish a new generalized $ \xi^{\ast } $-Kannan type double controlled contraction on a sequence and obtain fixed point results for a pair of multivalued mappings in left $ K $-sequentially complete double controlled dislocated quasi metric type spaces. New results in different setting of generalized metric spaces and ordered spaces and also new results for graphic contractions can be obtained as corollaries of our results. An example is presented to show the novelty of results. In this paper, we unify and extend some recent results in the existing literature.

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