Interpolative contractions and intuitionistic fuzzy set-valued maps with applications

Mohammed Shehu Shagari; Saima Rashid; Fahd Jarad; Mohamed S. Mohamed; Mohammed Shehu Shagari; Saima Rashid; Fahd Jarad; Mohamed S. Mohamed

doi:10.3934/math.2022600

AIMS Mathematics

2022, Volume 7, Issue 6: 10744-10758. doi: 10.3934/math.2022600

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Research article

Interpolative contractions and intuitionistic fuzzy set-valued maps with applications

1.
Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria
2.
Department of Mathematics, Government College University, Faisalabad, Pakistan
3.
Department of Mathematics, Çankaya University, Ankara, Turkey
4.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
5.
Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
6.
Department of Mathematics and Statistics, College of Science, Taif University, P.O.Box 11099, Taif 21944, Saudi Arabia

Received: 11 December 2021 Revised: 20 March 2022 Accepted: 24 March 2022 Published: 31 March 2022
MSC : 46S40, 47H10, 54H25

Over time, the interpolative approach in fixed point theory (FPT) has been investigated only in the setting of crisp mathematics, thereby dropping-off a significant amount of useful results. As an attempt to fill up the aforementioned gaps, this paper initiates certain hybrid concepts under the names of interpolative Hardy-Rogers-type (IHRT) and interpolative Reich-Rus-Ciric type (IRRCT) intuitionistic fuzzy contractions in the frame of metric space (MS). Adequate criteria for the existence of intuitionistic fuzzy fixed point (FP) for such contractions are examined. On the basis that FP of a single-valued mapping obeying interpolative type contractive inequality is not always unique, and thereby making the ideas more suitable for FP theorems of multi-valued mappings, a few special cases regarding point-to-point and non-fuzzy set-valued mappings which include the conclusions of some well-known results in the corresponding literature are highlighted and discussed. In addition, comparative examples which dwell on the generality of our obtained results are constructed.
- interpolative contraction,
- intuitionistic fuzzy set,
- fixed point
Citation: Mohammed Shehu Shagari, Saima Rashid, Fahd Jarad, Mohamed S. Mohamed. Interpolative contractions and intuitionistic fuzzy set-valued maps with applications[J]. AIMS Mathematics, 2022, 7(6): 10744-10758. doi: 10.3934/math.2022600

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Abstract

Over time, the interpolative approach in fixed point theory (FPT) has been investigated only in the setting of crisp mathematics, thereby dropping-off a significant amount of useful results. As an attempt to fill up the aforementioned gaps, this paper initiates certain hybrid concepts under the names of interpolative Hardy-Rogers-type (IHRT) and interpolative Reich-Rus-Ciric type (IRRCT) intuitionistic fuzzy contractions in the frame of metric space (MS). Adequate criteria for the existence of intuitionistic fuzzy fixed point (FP) for such contractions are examined. On the basis that FP of a single-valued mapping obeying interpolative type contractive inequality is not always unique, and thereby making the ideas more suitable for FP theorems of multi-valued mappings, a few special cases regarding point-to-point and non-fuzzy set-valued mappings which include the conclusions of some well-known results in the corresponding literature are highlighted and discussed. In addition, comparative examples which dwell on the generality of our obtained results are constructed.

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