Paired-Chatterjea type contractions: Novel fixed point results and continuity properties in metric spaces
Introduction/purpose: The paper deals with Paired-Chatterjea type contraction mappings as an extension of traditional Chatterjea type contractions that operates on three points rather than two, in the framework of standard metric spaces. Methods: The concept of Chatterjea type contraction mappings i...
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University of Defence in Belgrade
2025-04-01
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| Series: | Vojnotehnički Glasnik |
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| Online Access: | https://scindeks.ceon.rs/article.aspx?artid=0042-84692502423C |
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| author | Deep Chand Yumnam Rohen Sanasam Surenda Singh Nicola Fabiano |
| author_facet | Deep Chand Yumnam Rohen Sanasam Surenda Singh Nicola Fabiano |
| author_sort | Deep Chand |
| collection | DOAJ |
| description | Introduction/purpose: The paper deals with Paired-Chatterjea type contraction mappings as an extension of traditional Chatterjea type contractions that operates on three points rather than two, in the framework of standard metric spaces. Methods: The concept of Chatterjea type contraction mappings is employed in a metric space on three points rather than two using the idea of paired contraction mappings. Results: A series of corresponding properties has been discussed. Furthermore, it is established that Paired-Chatterjea type mappings form a distinct class from traditional Chatterjea type mappings and obtain at least one fixed point in the absence periodic points of prime period 2 within complete metric spaces. It is also demonstrated that how additional criteria to these mappings, such as continuity and asymptotic regularity, broaden the scope of fixed point results. Extending beyond Chatterjea's foundational contributions, two additional fixed point results applicable to Paired-Chatterjea type mappings in metric spaces are established, even in scenarios where completeness is not required. Conclusions: Paired-Chatterjea type mappings are generally discontinuous; they exhibit continuity at fixed points similar to Kannan and Chatterjea type mappings. In the absence of a periodic point of prime period 2, these mappings have a fixed point within the complete metric space. |
| format | Article |
| id | doaj-art-184eb51be5254d3c94f40dbef63462e5 |
| institution | DOAJ |
| issn | 0042-8469 2217-4753 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | University of Defence in Belgrade |
| record_format | Article |
| series | Vojnotehnički Glasnik |
| spelling | doaj-art-184eb51be5254d3c94f40dbef63462e52025-08-20T03:07:27ZengUniversity of Defence in BelgradeVojnotehnički Glasnik0042-84692217-47532025-04-0173242344910.5937/vojtehg73-54620Paired-Chatterjea type contractions: Novel fixed point results and continuity properties in metric spacesDeep Chand0https://orcid.org/0000-0002-9274-620XYumnam Rohen1https://orcid.org/0000-0002-1859-4332Sanasam Surenda Singh2https://orcid.org/0000-0002-3004-4499Nicola Fabiano3https://orcid.org/0000-0003-1645-2071National Institute of Technology Manipur, Department of Mathematics, Langol, Imphal, Manipur, Republic of IndiaNational Institute of Technology Manipur, Department of Mathematics, Langol, Imphal, Manipur, Republic of India + Manipur University, Department of Mathematics, Canchipur, Imphal, Manipur, Republic of IndiaNational Institute of Technology Manipur, Department of Mathematics, Langol, Imphal, Manipur, Republic of India University of Belgrade, ”Vinča” Institute of Nuclear Sciences - National Institute of the Republic of Serbia, Belgrade, Republic of SerbiaIntroduction/purpose: The paper deals with Paired-Chatterjea type contraction mappings as an extension of traditional Chatterjea type contractions that operates on three points rather than two, in the framework of standard metric spaces. Methods: The concept of Chatterjea type contraction mappings is employed in a metric space on three points rather than two using the idea of paired contraction mappings. Results: A series of corresponding properties has been discussed. Furthermore, it is established that Paired-Chatterjea type mappings form a distinct class from traditional Chatterjea type mappings and obtain at least one fixed point in the absence periodic points of prime period 2 within complete metric spaces. It is also demonstrated that how additional criteria to these mappings, such as continuity and asymptotic regularity, broaden the scope of fixed point results. Extending beyond Chatterjea's foundational contributions, two additional fixed point results applicable to Paired-Chatterjea type mappings in metric spaces are established, even in scenarios where completeness is not required. Conclusions: Paired-Chatterjea type mappings are generally discontinuous; they exhibit continuity at fixed points similar to Kannan and Chatterjea type mappings. In the absence of a periodic point of prime period 2, these mappings have a fixed point within the complete metric space.https://scindeks.ceon.rs/article.aspx?artid=0042-84692502423Cmetric spacefixed pointchatterjea type mappingspaired contractionpaired-chatterjea type mapping |
| spellingShingle | Deep Chand Yumnam Rohen Sanasam Surenda Singh Nicola Fabiano Paired-Chatterjea type contractions: Novel fixed point results and continuity properties in metric spaces Vojnotehnički Glasnik metric space fixed point chatterjea type mappings paired contraction paired-chatterjea type mapping |
| title | Paired-Chatterjea type contractions: Novel fixed point results and continuity properties in metric spaces |
| title_full | Paired-Chatterjea type contractions: Novel fixed point results and continuity properties in metric spaces |
| title_fullStr | Paired-Chatterjea type contractions: Novel fixed point results and continuity properties in metric spaces |
| title_full_unstemmed | Paired-Chatterjea type contractions: Novel fixed point results and continuity properties in metric spaces |
| title_short | Paired-Chatterjea type contractions: Novel fixed point results and continuity properties in metric spaces |
| title_sort | paired chatterjea type contractions novel fixed point results and continuity properties in metric spaces |
| topic | metric space fixed point chatterjea type mappings paired contraction paired-chatterjea type mapping |
| url | https://scindeks.ceon.rs/article.aspx?artid=0042-84692502423C |
| work_keys_str_mv | AT deepchand pairedchatterjeatypecontractionsnovelfixedpointresultsandcontinuitypropertiesinmetricspaces AT yumnamrohen pairedchatterjeatypecontractionsnovelfixedpointresultsandcontinuitypropertiesinmetricspaces AT sanasamsurendasingh pairedchatterjeatypecontractionsnovelfixedpointresultsandcontinuitypropertiesinmetricspaces AT nicolafabiano pairedchatterjeatypecontractionsnovelfixedpointresultsandcontinuitypropertiesinmetricspaces |